{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "134e7f9d",
   "metadata": {},
   "source": [
    "# Demo 6: Training Hyperparamters\n",
    "\n",
    "Regularization helps interpretability by making KANs sparser. This may require some hyperparamter tuning. Let's see how hyperparameters can affect training"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6459e11a",
   "metadata": {},
   "source": [
    "Load KAN and create_dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c3faa4ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1000, 2]), torch.Size([1000, 1]))"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from kan import KAN, create_dataset\n",
    "import torch\n",
    "\n",
    "f = lambda x: torch.exp(torch.sin(torch.pi*x[:,[0]]) + x[:,[1]]**2)\n",
    "dataset = create_dataset(f, n_var=2)\n",
    "dataset['train_input'].shape, dataset['train_label'].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2571d531",
   "metadata": {},
   "source": [
    "Default setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "97111d75",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 1.69e-01 | test loss: 1.50e-01 | reg: 5.01e+00 : 100%|██| 20/20 [00:12<00:00,  1.59it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train the model\n",
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.1);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07f400a8",
   "metadata": {},
   "source": [
    "### Parameter 1: $\\lambda$, overall penalty strength. \n",
    "\n",
    "Previously $\\lambda=0.1$, now we try different $\\lambda$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9916490a",
   "metadata": {},
   "source": [
    "$\\lambda=0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "77e8cafd",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 4.16e-03 | test loss: 5.00e-03 | reg: 1.24e+01 : 100%|██| 20/20 [00:10<00:00,  1.86it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MaxSp0+mg1+u5AkeJROIW6yhdwTAMTp06he3btwvCcJIvPEFcgGudmC1btmDnzp3IzMzE888/LygnBFtQKBSckaZSqURAQABXP+Ou38lTIOLiIly54ZYj0Wq12LJlC3JzczFp0iT84Q9/EHT2mi14iriwXL58GR988AHMZjOee+45jBkzxtUh9Yjm5mbOSNNgMCAiIoLb6IwYaTofIi5OpDujSIlE4hFzxuXl5fj666+h1WqxYsUKjB492tUh8YqniQtwLYPv448/xvnz5zF37lw88sgjbjkF2xmaplFTUwOpVIrq6mrOSDMlJQUJCQmCrf3yNIi4OBjWKFKn03HrKEIxiuQLmqaxf/9+ZGdnIzExEatWrfLIvT08UVyA/zPA/OabbxATE4MXX3wR8fHxrg6LF1gjzdLSUjQ2NnJGmikpKYiNjXXrWQKhQ8TFAbiDUSRfdHR04Ouvv0Z5eTnmzp2LuXPneuwN66niwlJdXY333nsPTU1NWLVqFWbPnu1R16pKpeKMNOVyOSQSCbfRGTHS5B8iLjzhTkaRfHHx4kV8//338PX1xapVq9wqtdUePF1cgGs9/W+++Qa//PILxo8fj2eeecYjjSVbW1s5I02dTofQ0FBuozNP/L6ugIhLD3Eno0i+MBgM+Omnn5CTk4ORI0fioYceErThJF/0BnFhOXPmDD755BP4+vrihRdeQHp6uqtDcgg0TaO+vh5SqZQz0oyOjuYKNT1l6toVEHGxA3c0iuSL2tpabNiwAR0dHfjDH/6ASZMmeeSorCt6k7gA1www33//fRQWFuK+++7D0qVLPbbDBFxLuKmsrIRUKkV9fT0oiuI2OouPj/fY6V5HQcTFStzVKJIvGIbB0aNHsXPnTkRHR2P16tW9zlCwt4kLcO2637FjB7Zu3Yrk5GSsW7fObYxGe4JGo0F5eTlKS0vR3t7OGWmmpKT0iu/PB0RcbkFno0iDwQCGYbgCR09dR+kKlUqFb7/9FgUFBZg+fToWL17sEanTttIbxYXl6tWrWL9+PVQqFZ5++mlMnTrV1SE5jY6ODq5QU6PRIDg4mCvUJEaa3UPEpQsMBgNXNd95HcWdjCL5oqioCBs3bgTDMHjkkUc8du7dGnqzuADXCmQ///xzHD9+HNOmTcMTTzzRq8wjWSPN0tJSVFRUwGQyoU+fPkhJSUFSUhL8/PxcHaKgIOLyv3iKUSRfmM1m7N69G4cPH0ZaWhoeffRRtzWc5IveLi7AtQfsb7/9hi+++AJhYWF48cUXMWjQIFeH5XTMZjOqq6shlUpRW1sLAJyR5oABA3rlM+NGerW40DTNCUpno0iJRNIr1lG6o7m5GRs2bEB9fb1HGE7yBRGX/6OxsRHvvfceKisr8dBDD2HhwoW99hrR6/XcRmctLS0Qi8WckWZ0dHSvbZdeJy5dGUWy9SjuahTJFwzD4PTp09i+fTtCQ0OxevVqj6nU5gMiLtdjNps5A8zhw4fj+eef7/XtolAoUFpaCqlUCpVKhcDAQAwaNAgpKSm9rm16jbh4qlEkX2i1WmzduhXnz5/HxIkT8eCDD/bq0VtXEHHpGtYA02Kx4LnnnvM4Tzl7aWpqglQqvc5Iky3U7A11YR4tLp5uFMkXrOGkRqPBQw89RB4O3UDEpXsUCgU+/vhj5ObmYt68eVi5ciUpQPxfLBYLamtrUVpaiurqajAMwxlpDhw40GNr4zxOXDxtwy1HQtM0fvnlF2RnZyMhIcFjDSf5gojLrWEYBvv27cO3336L2NhYvPTSS4iLi3N1WILCYDCgoqICUqmUM9JMSEhAcnKyxxlpeoS4sOsovcEoki9kMhm+/vprlJWVebzhJF8QcbGOqqoqvPvuu2hpacHq1asxa9Yscg92gUql4upn5HI5/P39OSPNyMhIV4fXY9xaXBiGgUwmu8ko0s/Pjzwob0F+fj6++eabXmM4yRdEXKzHYDDg66+/xsGDBzFhwgQ8//zzpA7kFrS2tqK0tBRlZWXQ6/UICwvD2LFjMXDgQFeHZjeCFBdbQpLL5fDx8bFrYd6TelO2tllDQwOSk5Ntnu/1pDYDbGs3jUaDK1euIDMz0+adDT2p3Wxps46ODrS3t9vVgfGkNgOsaze2w9zS0oI+ffrYtVWzUNpNkOKiVCp5XeRiGOamBrdYLAgMDOTtHK4mKyvrtvPbBoOhRxlgKpXK42w/CgoKEBoaatV7WX85WzoyZrMZZrPZowoNt23b5tAetdFohE6nw9133+2wc7iC3Nxch65pms1mmEwmpKWlOewctiDIlCmz2czbngp6vR4qlQpisfi6h0hHR4dHiUtTUxPmzp3b7f/37t2LvLw8pKenY/HixXad46uvvvI4cVEqlQ67GWmaxqFDhxASEuJR4lJXV4cHHnjAIceWSqX44osv0K9fP48TF5lMhpEjRzrk2EajEXv37kVoaKhgxEWwCxMURfX4BVwTkZCQEK5wsvP/PAmKoiASibp8Xb58GUePHsWKFSvw22+/obS0tNv33urlqdjTFta8ZDIZNBqNq7+eQ/Dy8uL9RVEU/v73v2PRokWu/noO4Vb3aE9f58+fF1x5hec+MXAt997Hxwe+vr6IiIiATCazab7YE2AYBhs2bMAzzzyDQYMG4fHHH8dnn33W69rBFVRWVto1Z95b2b59OwIDAz1udOwMSkpKcMcdd7g6jOvwWHFhGAYajQYRERGgKIqrcaFp2sWROZfCwkJ4eXlxC6qZmZkwGo1QqVQujszzqa+vR1JSkqvDcAtUKhV+/PFH/Pvf//bImQVHwjAMaJoWXEfGY8WFFRF2Oofd3Kujo8OVYTmdDRs24NFHH+VuWIqiMHr0aHz99dcujszzMRqNiI6OdnUYgodhGPzlL3/BrFmzPKK+w9m0trZCJBIJTpQ9Vlw6Ojpu2tArNDQURqPRhVE5F4vFAr1ej+HDh1/39+XLl+Pq1atkaswJEFeI23Pq1Ck0NTXhySefdHUobsnRo0cxYsQIV4dxEx4rLkaj8aYUU1ZoestD9dixYwgLC7upR8MWs+n1eleE1StgrzGh9SaFhsFgwPr16/H3v/8dXl5erg7H7WAYBgqFgoiLs+juxmYzxXQ6nSvCcjp79uzBY489dtPfKYpCQkICduzY4YKoege9aYRsLwzD4M0338TIkSMxZMgQV4fjlrBrp0IUZo8UF5VKxaU23khwcDAUCoULonIuDMPAZDJ1W1+xcuVKnDp1yslR9R4qKyttruLvbZw4cQJSqRR//vOfyQjPTg4dOiTYrcc9Vly6834KCAjwWIvrzpSXl8PHx6fbm7Zv376gadpqSwqCbVy9ehWpqamuDkOwKBQKvP/++3jjjTd6xf3oCBiGQXt7O8aNG+fqULrE48SFfRDeaiG1N9jKb9y48ZYV+xRFwcvLCzU1Nbc8jkqlwnfffQeZTMZ3iB6NXq93a9NBR0LTNF555RXcfffdRIB7QGVlJXx8fARXPMniceJiNpsBdL+Q6qkV+p1hezQzZsy45fumTZuGTZs23fI97733HnQ6Hd5//30+Q/Ro2A6OEOfBXQ3DMPjiiy9AURQef/xxj78XHQXDMDh27Nht73FX4nHiIpPJesUWordCqVQCwG17NHPnzkV9fX23/zeZTGhubsYTTzyB+++/n9cYPRmVStUrOjH2cPz4cRw7dgxvv/22R1sKORq5XA6LxYL+/fu7OpRu8ahfl13EDgkJcXUoLmXjxo1WbVXMOiRbLJYu/793717ExsbCy8sLmZmZvMboyZw/f55MiXVBWVkZPvroI7z11lu8GdP2RhiGQVZWFiZMmCDoDozHiQvQu2sLGIZBSUkJli9fftv3UhSF4OBgnDx5ssv/HzlyBKtWreI7RI+GYRi0tbXdVLja22lubsZf/vIXPP300xg8eLCrw3FrysvLYTKZBJslxuJR4sIaVfZWcWEYBkVFRRCLxVbv+rds2TLs2rWry2PRNE3sS2yErW8hGVD/R0dHB1566SXce++9mDFjRq+9P/lAq9Xi6NGjmDt3ruDbUZhpBnbAMAy0Wi369u3r6lBcxpEjR7B3716bFkozMzOh0+lu2lCtrKysVwu1vZw+fRpxcXGk3f6X5uZmvPLKK7jjjjuwbNky0i49QK/XY9euXUhPT3eL55zHjFzYdYPenKFTUlKCiRMn2jRcZveDaGhouO7vmzZtwj333MN3iB4NTdNobm7G2LFjXR2Ky2EYBsXFxVi3bh2mTZuGxx57jAiLnTAMg9bWVuzcuRMxMTGCX2th8ZiRS3t7OwICAtyi0R3FH//4R7uylGbNmoWvvvoKf//73wH838U8c+ZMB0TpuVy5cgVBQUG9fkrMZDJh//792L59O1auXInZs2f36vvSXhiGgUqlQkFBAUpLSzFs2DAMHz7cbdrSbcSFYRhu6ubGxqVpGmazGX369HFRdMLA3tTOuXPn4sCBA1z7srsnCrU4yxHc6EJg6w2s1+tx9epV3HvvvXyG5VbQNA2pVIpNmzZBLpfj73//O1JSUtzmYehq2GecTqdDU1MTKioq0NzcjL59+2L+/PkIDw93q7YU7NPDZDJxDzez2QyFQgGLxQKxWIzg4GBu/wI2O8ff39+tGl5I+Pj4IDAwECdOnMCUKVOwceNGjBgxote0Z1lZGdra2mAymeDl5YWAgAAEBQUhMDAQEokEvr6+8Pb27nZUaDKZcOTIESQnJ0MikbjgG7gOhmFgNptRXl6OrKwsFBYWYtasWVi0aFGvawtbYBNmLBYLDAYDVCoVmpub0dDQAIVCAYlEgvj4eIwePRqhoaFueS8KVlxaW1sRHh4Os9kMpVKJwMBA+Pn5Qa1Wo6WlBSEhIfD19YVGo4HFYkFUVJSrQ3Zr1qxZg3//+98YOnQoCgsL8cEHH7g6JKdRW1uLfv36wdfXF2azGWq1GrW1tdDpdLBYLKAoCn5+fggJCUFkZCRCQ0Ph6+sLhmEgl8uRl5eH4OBgQdqeOwqFQoG2tjYUFhbi9OnTaG1txaRJk/D222+jT58+bvkwdAYajQbV1dVobGyESqWC0WiE2WyGj48PwsLCkJCQgOjo6Os60O6KYMUlNDQUCoUCFEUhPDwcvr6+oCgKYWFh0Ov1UCqVUCqVoCgKUVFRbv0jCIH+/ftj1KhReO+99zBhwoRe1eu84447rhuVsNMTNE3DZDJBp9NBrVajo6MD5eXl123ZIBKJkJCQ0Oumf1555RUAQGxsLKZPn47Ro0cjJCSkV7WBPezatQuhoaGIi4tDYmIi/P39IZFIIJFIuNGxpyBYcRGJRAgKCuIa22AwcP+jKApBQUGwWCzw9vaG2WzmPMWsxdPWE7y8vJCfn9+jY4wZMwbx8fHo27dvl8fyRMNPkUiEpqam277P29sbffr0QWRkJEwmE4xGIzei8fb2vuUxPM2OyNvbGzNnzkRYWBgCAgIgEolQVlbG6zk8cf1UJBIhJSXlupGdXq+HXq/nzRhWSM4HFCNAP3VnheRJvQRnbE4lEok8TpRt7ZTYA+tA7Sl07ug5CpFI5HFZd73tWhOkuNgCu6DoaUNKR2KxWKDVauHv7y+YC9EdoGmaazdiumgdFosFer0efn5+5FqzAYvFAp1OB4lE4rbt5vZ3iNlsRktLi1N6BZ5CfX09XnzxxVs6IhNuRqFQYN++fb1iJ1O+qKqqwrJly1BVVeXqUNwKmUyGLVu2uPU+Sm4vLgQCgUAQHkRcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7RFwIBAKBwDtEXAgEAoHAO0RcCAQCgcA7bi0uDMOgra0NtbW1aGtrA8Mwrg5J8DAMg46ODqhUKnR0dJA2sxKGYdDe3o7W1la0t7eTdrMC9lrTarXkWrMB9lpjX27bbowbIpPJmA8//JBJSkpiAHCvpKQk5sMPP2RkMpmrQxQcpM3sg7Sb7ZA2sw9Paze3E5cDBw4wAQEBDEVRDEVR1/0I7N8CAgKYAwcOuDpUwUDazD5Iu9kOaTP78MR2cytxOXDgAOPl5cWIRKLrGv/Gl0gkYry8vNzqh3AUpM3sg7Sb7ZA2sw9PbTeKYdxjQk8ulyMuLg46nQ40Td/2/SKRCBKJBHV1dQgNDXV8gAKEtJl9kHazHdJm9uHJ7eY2C/rfffcdtFqtVT8AANA0Da1Wi02bNjk4MuFC2sw+SLvZDmkz+/DkdnOLkQvDMEhOTkZFRYVNmRMURSExMRFSqRQURTkwQuFB2sw+SLvZDmkz+/D0dnMLcWlra0NUVFSPPh8REcFjRMKHtJl9kHazHdJm9uHp7eYW02JqtbpHn1epVDxF4j6QNrMP0m62Q9rMPjy93dxCXAIDA3v0+aCgIJ4icR9Im9kHaTfbIW1mOyqVCiUlJT06htDbzdvVAVhDREQEkpKSbJ6bBICBAwdCJBJBq9XCx8cHPj4+DopSWPSkzeLj4+Hl5QWGYQQ9p+sIIiIiMHDgQFRVVdn82aSkJISHh/MflICpq6tDdnY2AgICoNFobPosu3bQW9pMJpOhoKAA+fn5qK6uBgBERUWhtbXVpuO4S7u5hbhQFIVnn30Wa9eutflza9asgZ+fH4xGIwwGAyiKgo+PD8RiMby9vT324WlvmwHAI488gvr6ejQ3NyMsLAxhYWG9QpR1Oh0uX76MyZMn2yUuy5Yt89jrqTMWiwVnzpxBdnY2Ll68iODgYMyfPx/bt2+3+Vhr1qzx6DZraWnhBKW+vh5eXl5ISUnB/fffj7S0NMTExGDt2rU2dwDdod3cYkEf4Ccf3GKxwGg0wmQywWKxgKIoeHt7QywWw8fHR/A/lq3I5XLExsZCp9NZdfF2bjOJRAKZTAaZTAaaphEUFITw8PAeT4EIEZqmUVJSgoKCAlAUhYSEBNxxxx3Q6/VWXWsURUEsFuPNN99EcnIypk6dKuiFVnvp6OjAL7/8gv3796OtrQ1DhgzB/PnzMWXKFGi1WpvuT4qiIJFIUF9fL/h6DVtgGAYNDQ2coLS0tEAsFiM1NRUZGRkYPHgw/Pz8uPd7cp2L24gLABw8eBBz584FTdO3fFiKRCJQFIX9+/dj1qxZXb7HYrHAZDLBZDLBbDYDADdtJhaLPUJoNBoNsrKysHz5cgC45cXbXZvRNA2FQoGOjg7o9XqIxWJuNOPl5eXw7+Bo6uvrceHCBajVaqSkpCAzMxNisZi71hiGsbrdBg8ejBMnTkAul2Po0KEYP378dQ8Sd4RhGOTn5yMrKwsnT56Et7c3pk+fjnnz5iEpKem691rbZuy99fTTT+Nf//oXgoODHfodHA3DMKiuruYERSaTQSKRIC0tDRkZGUhOTr7lyN+ea62755qQcCtxAa79EIsWLYJOp7vpf+xF6+/vj507d1r9A9A0DZPJBKPRyAlN5xGNSOQWeQ/XoVarodFoEBAQgJMnT2LJkiXQarUAcJ0w29JmOp0OHR0dUCgUAICQkBCEh4dDIpE48Js4BoVCgQsXLqCxsRHR0dEYNWoUQkJCrnvPwYMHbW43mqaRn5+Ps2fPgqIojB07FhkZGW53DWk0Gvz666/Izs5GTU0N4uPjMW/ePMyYMQMBAQHdfs7aNvvuu+9QW1sLiqLw8MMPIywszLFfiGcsFgsqKiqQn5+PwsJCqFQqBAYGIj09HRkZGUhMTLSp83WrdgOutZ2tzzVX43biAgBfffUVfvjhB1RWVqKiooL7e1JSEtasWYOVK1fe9KCwFoZhuKkzk8kE4JrQsCMad3hIsMISGBjIPQjkcjk2bdqEjz/+GOXl5dx77Wkzi8XCTZkZjUb4+fkhPDwcISEhgm8fo9GIK1euoLS0FAEBARg1ahTi4uK6fb+97abT6XD27FkUFBQgLCwMU6ZMQXx8vEO+E5+Ul5cjOzsbR44cgdlsxqRJkzB//nxkZGRYPZq3ts0UCgW+++47mM1mrFy5UvBTiWazGaWlpcjPz0dRURF0Oh3CwsI4QYmPj+/R9d9du8XExGDdunVYtWqV3c81V+B24kLTNF566SVMmDABS5Ys4fYmYdcE+JzOYhjmuhENwzDw8vLihEaI00IqlQparRZBQUHw9/e/6f9Mp/1c+GgztVrNHc/LywuhoaEICwuDr69vT74G7zAMA6lUisuXL4NhGKSnpyM1NdXqh4G97dbW1oacnBzU19dj4MCBmDx5suDmyo1GI3JycpCVlYXi4mJERkZizpw5uOeee3qUkWRNm6lUKmzatAk6nQ4PP/ww+vTp09OvwysGg4FbjysuLobRaESfPn2QkZGB9PR0xMTE8D6F3rndJBIJpFIpEhMTERMTw+t5HI3biUtRURE+/PBDvPbaa07tCTIMA7PZzI1qGIaBSCTips68vV2feKdUKqHT6RAcHOz0qSqTyYSOjg7I5XKYzWYEBAQgPDwcQUFBLl+/ampqwoULFyCXy5GUlIRhw4Y5vX3Kyspw8uRJaDQaDBs2DGPGjIFYLHZqDDfS2NiI/fv348CBA1AqlRg5ciTmzZuH8ePHO7XjpNFo8P3330OpVOKhhx5CdHS0087dFVqtFkVFRcjPz4dUKoXZbEZsbCw3QnG2ABYVFcFsNiMzM9Op5+0pbicu3377LcrKyvDWW2+59KHFTpsZjUZOaDqnODsbhUIBvV6PkJAQly4iMwwDpVLJ7UDo7e3tsnRmtVqNixcvora2FlFRURg1apRLp17MZjMuXbqECxcuwMfHBxMmTMCQIUOceh3TNI3z588jOzsb58+fR0BAAGbNmoW5c+fecnrQ0eh0OmzevBnt7e1YsWKF02NRKpUoLCxEfn4+Vxs2YMAAboTiyjWh1tZWXL16FWPGjBHcjMCtcCtxMZvNeOGFFzBjxgzce++9rg6Ho/OIhqZpLjXVGUWbDMNAoVDAYDC4XFhuRK/XQyaTQS6Xg2EYbmrkVgvCfGA2m1FYWIiioiL4+flhxIgRGDhwoEPPaQtqtRqnT5/G1atXERUVhalTpzq8ty6Xy3Hw4EFkZ2ejpaUFKSkpmD9/Pu644w7BPLAMBgO2bNmCpqYmLF++HAMGDHDo+To6OrgMr5qaGlAUhaSkJGRkZCAtLU0wWWwWiwVnz55FfHy8SzsAtuJW4pKXl4fPPvsMb7zxhsuHzt1hNpu5EQ0rNKzI8F1LwwqL0WhESEiIYB4SN0LTNORyOTo6OmAwGODr64uwsDCEhobyOv3CMAwqKyuRl5cHo9GItLQ0pKWlCWLKsisaGxuRk5ODlpYWJCcnY+LEibxaejAMg6KiImRlZSEnJwcikQh33nkn5s+fj5SUFN7OwydGoxHbtm1DXV0dli5disTERN6OzTAMWlpakJ+fj4KCAjQ0NMDb2xspKSnIyMjAkCFDulynFAIlJSXQ6XQYMWKEq0OxGrcSl//+979oamrC66+/7upQrIKtpTEajbwXbTIMA7lcDpPJhNDQUJfP31uLVqtFR0cHlEolKIpCSEgIwsLCerwG0tbWhtzcXLS3t2PAgAEYMWKEw0dIfMAwDEpKSnD69GkYjUaMHDkSI0eO7JEg6nQ6HD16FFlZWaisrERMTAzmzZuHWbNmCd6PCrg25fzjjz+isrISDzzwQI+EkGEY1NfXc4LS2toKsViMIUOGICMjA6mpqW5x77S3t6O4uBijRo1ym9R/txEXg8GAF154AfPnz8fdd9/t6nBshqZpbursxqJNW2tp3FVYOmM2m7l0ZpPJBIlEgvDwcAQHB9vUFjqdDpcuXUJlZSXCwsIwevRowWUcWYPRaERubi4uX74MiUSCSZMmITk52aZjVFdXIzs7G4cPH4Zer8eECRMwf/58jBgxwuVJFbZiNpuxY8cOlJaWYsmSJUhLS7P6szRNX1fUKJfL4e/vf11Ro1BHs91B0zTOnj2L2NhYt0hpB9xIXM6dO4cNGzbgX//6l+Dz4W9HT4o2GYaBTCaD2Wz2CM8vhmG4dGa1Ws2lM4eHh99SNC0WC4qLi1FYWAgvLy8MHz4cSUlJbvcQvRGFQoETJ06gsrIS0dHRmDp16i33/DCbzTh58iSysrKQn5+PsLAwLo24J3uFCAGLxYLdu3ejsLAQCxcuvGW2lMViQXl5OVfUqFarERwcjKFDh3JFjUKvwbodpaWlUKlUGDVqlKtDsQq3EZdPP/0UKpUKr7zyiqtD4ZWuija9vLw4oem8JkHTNOf1FRoa6vbCciNGo5EbzVgsFgQGBnJ+Zp1Fo7a2FhcuXIBWq0VqairS09PdcvR2K2pra5GTk4OOjg6kpaVhwoQJ102HtLS0cGnEMpkMmZmZmD9/PiZOnOh2vfJbQdM0srKykJeXh/nz52PkyJHc/0wmE1fUWFxcDJ1Oh/DwcC7DKz4+3u07G52RyWQoLCzE8OHD3cLjzy3ERaPR4MUXX8T999+PadOmuToch8EWbbKvzkWb3t7eUCqVoGkaYWFhHvUAuRGaprl0Zp1OBx8fH4SFhYGiKFy+fBlNTU2IiYnBqFGjBJPR4whomkZBQQHOnj0LhmEwevRomEwm/PLLLzhz5gwkEglmzJiB+fPnu81UiT0wDIP9+/fj/PnzmD59OoKCgpCfn4+SkhKYTCb07duXE5To6GiPEpTOMAyDc+fOoW/fvoLKfuwOt3hCXbp0CTRNY/To0a4OxaGwKcxisfi6ok2tVguZTAaKotxyPcFWRCIRQkNDERoaCr1ej8bGRhw9ehTV1dVc6u6NpomeiEgkQmZmJvr164cvvvgCf/zjH6HRaJCZmYk1a9bgrrvucpvF3Z6g1WoRFRUFpVKJV199FQMGDMC4ceMwY8YMpKenu/30n7VQFIXIyEi0trYSceGLc+fOYfDgwR7dS70RNoVZJBJBp9MhICAAgYGBsFgsUKlULi/adAbswuyVK1fAMAymTJmCiIgI6PV6lJWVITw8HKGhoW4/l94VDMOgtLQUWVlZ+O2338AwDGbPno3IyEgA19Za9Hq9x4qLQqG4rqgRAAYNGoQBAwagoaEBw4YNw9SpUz12lNIdkZGRaGxshFKpFPzzUPBPJaVSiatXr+Khhx5ydShOhzWIBIA+ffpw6y+dizY9dQO0xsZGXLhwAQqFAoMGDcKwYcO4AlGNRoOOjg40NTWhubmZ8zMTUgGpvRgMBhw7dgxZWVkoKytD37598fDDD2P27NmcaWFFRQVOnDiBbdu2ISMjA2PHjhVsjZMttLe3X1fUKBKJMGjQICxevBhDhw7l1hlycnJw5MgRmEwmTJ8+3SOud2sJCQmBWCxGa2ur4MVF8GsuR48exU8//YT33nvPLeoW+IJN1RWJRAgLC+u2d97VBmiOKtp0BiqVChcuXEB9fT369OmD0aNHd2u9YTKZuAQAs9kMf39/Lp3Z3b43u13w4cOHodFoMGbMGMyfPx+jR4/u8re3WCzIy8tDbm4uvLy8MH78eAwdOtStvjfDMGhubuZqUBobG+Ht7Y3BgwdzRY3djczOnDmDAwcOYPz48Zg9e7Zbfe+eUllZiZaWFowdO1bQ31vw4vLvf/8bgYGBeOaZZ1wditOwVlhu5MaiTQDciEboQmMymVBQUICSkhJIJBKMHDnS6kVqhmGgUqnQ0dEBjUYDb29vLp1ZyBl17HbBWVlZuHTpEkJCQnD33Xdjzpw56Nevn1XH0Gg0OH36NEpKShAREYGpU6ciNjbWwZHbD8MwqKur4wSlra0Nvr6+SEtLQ3p6OgYPHmx15l9ubi6ys7MxatQozJs3T9DXN5+o1Wrk5eUhPT1dcA7bnRG0uLS3t+PVV1/F6tWrMXbsWFeH4xTY3jj7gLR3PYHPok1HwjAMKioqkJeXB5PJhKFDhyItLc1uWxiDwcD5mVksluv8zITy8Glvb+e2C25vb0daWhq3XbC9Ytjc3IycnBw0NTVh0KBBmDhxomCmTWiaRlVVFTflpVAo4O/vj/T0dKSnp2PQoEF2rxvm5eVhz549yMzMxIIFCwRzXTua3NxchISE2Fxo60wELS4HDhxAVlYW3n//fY+YU74dRqMRcrmccxLm62HYXdGmqzdAa21tRW5uLjo6OjBw4ECMGDGCN28noW3PzDAMLl++jKysLJw6dQpisZjbLpgv/yw2CeDUqVPQ6/WclYwrRm8WiwVlZWUoKChAQUEBNBoNQkJCuKLGhIQE3q67goIC7Ny5E0OGDMHixYsFuc8S31RXV6OxsRFjx44VrKAKWlzeeust9O3bF0888YSrQ3E4rLD4+PggNDTUYb3szhug3a5o01FotVpcunQJVVVVCA8Px+jRox2aTtrV9sxhYWFOMSlUq9XcdsG1tbWIj4/H/PnzMX36dIetIZpMJly4cAGXLl2Cn58fJk6ciMGDBzvkXJ0xGo3XFTXq9XpERERwNSj9+/d32HVdUlKCn376CYMGDcL999/vsRmULFqtFhcvXkRaWlqPNnRzJIIVF9ag8umnn3YrJ1B7MBgMUCgUEIvFCAkJcdr0za2KNh2x06bZbOYsW3x8fDB8+HAkJiY67fs6c3vmsrIyZGdn4+jRo3ZvF9xTlEolTp48ifLycvTr1w9Tp07lvU5Kp9OhpKQE+fn5uHr1KkwmE/r168cJSr9+/Zz2fcvKyrB9+3YMGDAADz74oKDX2/jg0qVL8Pf3d0rHwR4EKy579+7Fr7/+ivXr13v0RWIwGCCXy+Hr6+tUYbkRR++0WV1djUuXLkGn03GWLa78XTtvz8wWbYaHh/do+tVoNOL48ePIyspCSUkJIiMjMXfuXNxzzz0u3Wyqrq4OOTk5aG9vx5AhQzB+/PgejZrUajUKCwtRUFCAsrIyWCwW9O/fHxkZGRg6dKhLixorKyuxbds2xMTEYNmyZR5nC9SZuro61NTUYNy4cYKcChSkuDAMg9dffx2JiYl49NFHXR2Ow9Dr9VAoFPDz8+NqGIRC5xENTdNc0aatG6DJZDLk5uaipaUFcXFxGDlypKBs329MZ7Zne+bGxkZkZ2fj0KFDUCqVGDVqFObPn4+xY8cK5qanaRpFRUU4c+YMLBYLRo8ejeHDh1sdn1wu59ZPKisrAQAJCQmcoAgpa6mmpgZbtmxBnz59sHz5co+of+oKvV6P3NxcDB48WJAuBYIUl5qaGvzjH//Ac889h6FDh7o6HIeg0+mgVCohkUgEk9XTHd1tgHarok29Xo/Lly+jrKwMISEhGDVqlGA3eANs356ZpmmcO3cOWVlZyM3NRWBgIGbPno25c+cKOhXYYDDg3LlzyM/PR2BgICZPntxtQkFbWxuX4VVbWwsvLy8kJycjPT0daWlpgjZPrK+vx+bNmxEWFoYVK1YIdhOwnnL58mX4+PjYtCWBsxCkuOzYsQMnT57Ee++9J9hMiJ6g1WqhUqncQlhu5HZFmwzD4OrVq8jPzwdFUcjMzERycrJb/Y4GgwEdHR3Xbc8cFhaGwMBAyGQyHDhwAPv37xfsdsHWIJPJkJOTg5qaGsTFxWHKlCkIDw9HU1MTJyhNTU3w8fHhihpTU1Pdym6mqakJ33//PQIDA/HQQw8JWgztpaGhAZWVlRg3bpzgkhgEJy4Mw+DVV19FRkYGli9f7upweIcVFn9/f0FND9nDjUWbjY2NKCgogF6vR2pqKoYNG+ZWD9wb6bw9c0FBAXJycnDlyhX4+vpi2rRpmDdvnmC3C7aWyspK7NmzB1evXgVN05yHXeeiRnde82xtbcWmTZvg6+uLhx9+2O06c7fDaDTi3LlzSE5ORt++fV0dznUIS+oAlJeXo6OjwyOLJjUaDdRqNXcDuzteXl7w8vKC0WjExYsXUVNTg4iICIwdOxYhISEwGo0AIKiiTVvQ6/U4efIksrOzUV5ejoiICG7PlOjoaMGmgN4OmqZRWVnJbawlk8nAMAwoikJ4eDjmzZuHzMxMt/zNbiQqKgqPPvoovvvuO2zcuBErV64U1PpQT2EzTFtbWwUnLoIbuWzbtg15eXn497//LZiKaj5Qq9XQaDQIDAz0GI80o9HIpaAGBARg5MiR6N+/P1e02XkDNCEUbVpLZWUlsrOzceTIERgMBm674OHDh8NisXCjmZ5sz+xszGYzV9RYWFjIFTWyKcMDBw6EXq/HmTNnUFRUhPDwcEyZMgX9+/d3dei8IJfL8d1334GmaaxcudJtOwZd0dTUhLKyMowbN05Qo0xBiQtN03jppZcwfvx43H///a4OhzdUKhW0Wi2CgoI8YmGRYRiUl5cjLy8PFosF6enpSE1N7TLzSAhFm9ZgMplw4sQJZGdno6CggNsueM6cOZzNfWfs3Z7ZmRiNRm79q7i4GAaDAZGRkZygxMXFddmBa21txfHjx9HY2IiEhARMnjxZcNmM9qBUKrFp0yYYDAY8/PDDgsywsgez2YyzZ88iMTFRUEkzghKXoqIifPjhh/jLX/6CAQMGuDocXlAqldDpdAgODnarxdDuaGlpQW5uLmQyGRITEzF8+HCrv5ezizatgd0u+JdffoFcLsewYcMwf/58TJgwweoFUmu3Z3YGOp0OxcXF3IjSbDYjOjqaE5S+fftaHZNUKsXJkyeh0+kwbNgwjB49WjDCaS8ajQabNm2CWq3GQw89ZLVBqNApLCyExWJBZmamq0PhEJS4fPfdd5BKpXjrrbc8YkpMoVBAr9d7hLBoNBpuXSUyMhKjRo3qskdvLd0VbTpjAzSGYXDhwgVkZWXh7NmzkEgkmDVrFubOnduj7YIZhuH8zDpvz+zobanZosb8/HyUlZWBpmnEx8dzghIREWH3sc1mMy5evIiLFy9CLBZjwoQJSE1Ndev7U6vVYvPmzZDJZFixYoWgU8etpaWlBaWlpRgzZoxgkmgEIy5msxnr1q3DtGnTsGDBAleH02NYYQkJCXHrIi6z2YyioiIUFRVBLBZjxIgRGDhwIO8Pl85Cw9bSsFNnfM0jKxQKHDp0CPv27UNjYyOSkpIwf/583HXXXbz/Rnq9nvMzYxgGwcHBCAsL4229TSaTcUWNVVVVAICkpCSkp6dj6NChvE9jqVQqnDp1ClKpFH369MHUqVPdutev1+uxZcsWtLS0YPny5T3qVAgBi8WCs2fPIj4+HnFxca4OB4CAxCUvLw+fffYZ3njjDUHNG9oK23s1GAwIDQ0VTC/CHqqqqnDp0iXo9XqkpaVh6NChTsmlt6doszsYhkFJSQmys7Px+++/g2EY3HHHHZg/f75TeuAWi4UbzRgMBvj6+nJ+ZrZOA7a2tnI1KHV1dfDy8kJKSgpX1OiMRJGGhgbk5OSgtbUVgwcPxsSJE902QcVoNGLr1q2or6/HsmXLkJCQ4OqQekRJSQn0ej2GDx/u6lAACEhcvvrqKzQ2NuL11193dSh2wzAM5HI5TCYTQkJC3FZY2tvbceHCBbS2tqJ///4YOXKky1Kn7d1pU6/X49ixY8jOzkZZWRn69euHefPmYdasWS5bnGa3Z1apVKAoCiEhIQgPD+921MQwDFc7lJ+fj+bmZvj4+CA1NZUranTFqJhhGBQXF+P06dMwmUwYNWoURowYIbgiPmswmUz44YcfUFVVhT/84Q+C3h/ldrS3t6O4uBijRo0SxDS8IMTFYDBg3bp1nMmfO9JZWEJDQ91y4VOn0+Hy5csoLy9HaGgoRo0aJaipj+522mRHNRRFoba2ltsuWKvVYty4cZg3bx5Gjx4tmHUCdqfRjo6Om7ZnBq7ZH7E7NXZ0dEAikWDIkCHIyMhASkqKYNJNjUYjzp8/j8uXLyMgIACTJk3CoEGDXB2WzZjNZvz888+QSqW47777MGTIEFeHZBc0TePs2bOIjY0VxDSfIMTl3Llz2LBhA/75z3/2aJHYVTAMwxkfdudFJWRomuZs0728vDBs2DAMGjRIMA/jrui8AZper8f58+dx6NAhFBYWIjQ0lEsjFlphWWfY7ZlbW1tRWlqKsrIy1NfXcyNfdqfGpKQkwaRsd4VcLseJEydQVVWF2NhYTJkyxe3uY4vFgp07d6K4uBiLFy9Genq6q0Oyi9LSUqhUKowaNcrVoQhDXD799FMolUq8+uqrrg7FZliLEIvFgtDQULcTlrq6Oly4cAEajQYpKSnIzMx0m1FXW1sbfvnlF+zbtw/t7e1ITU3FzJkzMX78eEgkEkEXbZrNZkilUuTn56OoqAhKpRK+vr6Ij49HYmIiUlJSEBkZ6ZJ0ZnupqalBTk4O5HI5hg4dinHjxgliesZaaJrG3r17cfnyZSxYsEAwaxe2IJPJUFhYiBEjRrh8Lczlk6RarRYFBQW47777XB2KzdA0DZlMBpqmHZ5uyjcKhQK5ubloampCdHQ07rzzTrcolGMYBnl5ecjKysLp06fh6+vLbReckJBwXdGmXq+HTqcTTNGmwWBASUkJCgoKUFxcDKPRiKioKIwbNw4ZGRmIjY3lEkJkMhlqamrg4+OD8PBwhIaGCv76io+Px9KlS5Gfn4+zZ8+itLSU+25CFPgbEYlEWLBgAby9vbF7926YTCaMGTPG1WHZBHudtLa2ulxcXD5yOXnyJDZt2oR33nnHLR5uLO4qLEajEVeuXEFpaSkCAwMxatQot8jzV6vVOHz4MLKzs1FXV4cBAwZw2wV353rQVdEmnxugWYNWq+WKGktLS2E2mxEbG8tNefXp06fbkcmN2zMHBwcjPDzcLVwedDodzp49y01TTpkyRRDrANbAMAwOHjyIM2fOYPbs2ZgwYYKrQ7KJsrIyyGQylwujy8Xlgw8+AE3TWLdunSvDsAl2u1wACAsLE/R8OAvDMJBKpbh8+TIYhkFGRgYGDx4s+B6lVCpFdnY2jh07BovFgsmTJ2P+/PkYOnSozdNFrMgYjUaHFm2qVCquqLG8vBw0TWPAgAFcUaOtvlad/cwcvT0z37S1tSEnJwf19fUYOHAgJk+e7BbGkQzD4OjRo8jJycG0adMwdepUV4dkNQqFAvn5+cjMzHSpC7RLxUWpVOKll17CihUrMGXKFFeFYRPuKCxNTU24cOEC5HI5kpKSMHz4cEEXdhoMBm674KtXryIqKgpz587F3Xffzdt2wXwXbcpkMi7Dq7q6GhRFITExkdupka+b3BHbMzuD8vJynDhxAhqNBsOGDcOYMWPcYm3v+PHjOHr0KKZOnYq77rrLbda/zp07h8jIyG43gnMGLhWXY8eO4YcffsD69etdPj9oDWwKqUgkQlhYmOB7jWq1GhcvXkRtbS2ioqIwatSoHlmBOJqGhgZuu2CVSoXRo0dj3rx5GDdunEPb2t6izZaWFk5Q6uvr4e3tfV1RoyOnr7ranjksLAzBwcGCfQCazWbk5eUhNzcXPj4+mDBhAoYMGSLYeFlOnTqFQ4cOYcKECZg1a5bg4wWuOXu3tLRg7NixLovXpeLyzjvvQCKR4Nlnn3VVCFbjTsJiMplQWFiI4uJi+Pn5cZYtQsRiseDcuXPIzs5Gbm4ugoKCuO2CY2JiXBLPjUWb3t7enNA0NjZygtLS0gKxWIwhQ4ZwztDOHkGw2zPLZDJoNJrbbs8sBDQaDU6dOsWNSqdMmeKS39oWzp07h/3792PMmDGYM2eO4AVGrVYjLy8P6enpLpuGdJm4dHR04JVXXsFjjz2G8ePHuyIEqzGZTJDL5ZytulCFhWEYVFZWIi8vD0ajEWlpaUhLSxNksgG7XfC+ffvQ2tqK1NRUzJ8/H1OmTBHMFA8rNOXl5ZxtvVKpREBAADIyMrgtnIXyEO+8PTNN0wgKCuLcmYVIU1MTjh8/jpaWFiQnJ2PixImC3p310qVL2Lt3L4YNG4Z7771XsM8BltzcXISEhLjMdcBl4nLw4EHs3bsX69evF/T8Pzv9wPYIhdpjaWtrQ25uLtrb2zFgwABB5LnfCMMwKCgoQFZWFk6cOAFvb29uu2AhVXZbLBZUVFRwOzWqVCoEBARgyJAhSE5ORv/+/eHl5cWNaIS20yZN05yfmV6vh1gs5tKZhbZGyDAMrl69ilOnTsFgMGDUqFEYOXKkIDtEAJCfn49du3YhLS0NixYtElx7dqa6uhqNjY0YO3asS65Pl4nLP/7xD0RFReHJJ590xemtwmg0Qi6Xw8fHB6GhoYIUFq1Wi7y8PFRWViIsLAyjR49Gnz59XB3WdWi1Wvz666/Izs5GdXU14uLiMG/ePMycOVMwvWqTyXRdUaNOp0NYWBiX4TVgwADu92cYhps6E/pOm1qtFh0dHVAqlQDA+ZkJrbjRaDTiwoULyMvLg0QiwaRJkwTr81VUVIQdO3YgJSUFS5YsEawQarVaXLx4EWlpaS7ZedMl4tLU1ITXX38dTz31FEaOHOns01uFwWCAQqEQrLBYLBYUFxejsLAQXl5eGD58OJKSkgQVZ2VlJbKysnDkyBEYjUZMnDgR8+fPx7BhwwQRp8FgQHFxMQoKClBSUgKj0Yg+ffpwghITE3PbODsXbZrNZkFsgNYVZrP5pu2Zw8LCBJfOrFAocPLkSVRUVCA6OhpTpkwRXGcJuGaz8uOPPyIhIQEPPPCAYKZGb+TixYsICAjA4MGDnX5ul4hLVlYWDh8+jPXr1wvyRzEYDJDL5fD19UVISIggHoSdqampwcWLF6HVajmHXKG0I7tdcFZWFgoLCxEREYE5c+bg7rvvFoTflFarRVFREVfUaLFYEBcXd11Ro710twGaM4s2rYlR6NszA0BtbS1ycnLQ0dGBtLQ0jB8/XnDFoxUVFdi2bRvi4uKwdOlSQbUfS21tLWprazFu3Dind3ScLi4Mw+Bvf/sbEhIS8Oijjzrz1Fah1+uhUCjg5+cnOMcAuVyO3NxcNDc3IzY2FiNHjnRpkVRnmpubsW/fPhw4cAAKhQIjRozAvHnzMH78eJc/VJVKJVfUWFFRAYZhritq5Kt25kacVbRpLzduzxwQEIDw8HAEBQUJokNF0zQKCwtx5swZMAyDMWPGIDMzUzCjQeDausbWrVvRt29fLF++XDDJKCx6vR65ublITU11eufO6eJSW1uLt956C8899xyGDh3qzFPfFp1OB6VSKThhYRgG58+fR1lZGYKCgjBq1CjBpG7KZDJ88MEHOHfuHPz9/bntgvv37+/q0FBVVYV9+/ahuroaIpEISUlJXFGjs7OSuivaFEJvnE1n7ujogFarhY+PD6Kiohwmurai1+tx7tw55OfnIyQkBDNmzBDUVhB1dXXYvHkzIiIisGLFCsGtZ12+fJlLmXcmvIhLdna21f5USqUS1dXVSE9Pt7p3ZDKZYDAY7KriZ3P/rUGv18NkMt32wcMwzHWx0zRt1wWVn59vdQ56RUUF/Pz8EB0dfVO7mc3mbr+jwWCwKxNr8+bNVu3MxzAMysrKEBYWhvDw8Jvm79ndF7tCoVBgzpw5NsX166+/Wv1gUavVqKqqQmRkJCIiIripQ3b6qrupRI1Gg3HjxtkUF3Ctc0JR1G3XMMxmM7c+Y+t1wzCMXb3jlpYWq7Iy2bVGPz8/m0bFNE2Dpmm7Fo7PnTuH4ODg207tajQaVFRUICkpyWZR1uv1Nndmf//9d0RFRVn1nFKr1aioqLAp9Z/tcNhjj19TU2N1Nmh7ezv0er1NHoI0TcNisfRIxHkZmzc0NNi0ydfkyZOtfm9jYyO+//57hIeH2yUu7GZM1mDNnKlarYbRaISPjw9nh65UKu0SF4VCYfUF39WFwTAMCgsLUVdXh6CgIIwbN+6mC/vkyZN2iUt1dTUefPBBq97bXZ3Sjh07cOzYMYwYMQKrVq266f//+te/bBaX5uZm3HXXXVa//0bzPp1Ohx07dkAul2PkyJGYOHHiTZ/ZunWrXeJisVhgNpsRFBR0S4HpyfqYRqOxS1wMBgOioqJu+76goCCbp0/UajXa29u5lGdb6ejogFQqtep6s2e2o6ysDDU1NTZ/tqWlBY2Njbj//vuter8tyUl6vR5btmzhNuWzFa1Wi7i4OKvea+sI1GAwoLS0FL6+vj0SF17SRCiKgpeXF+8vkUiEjz/+uMcZZRRF8fLSaDQwGAwIDAzkzAR7ikgksutFURSuXLmC8vJyZGZmwmw249ixY1zPmX31pM28vb3tfl24cAGbN2/GypUrsX//fpw9e/am99hLT66nr776CiKRCNOmTcOhQ4eQl5d30/t6gq+vL1QqFdeGfL2Aa52JnsBnPOzLaDRy9kI9QS6Xc4XKfL5qa2vx+++/291epaWlUCqVvMf166+/9qiTQVEUWlpabrrf+XgVFxfzspYrnBzELqiuroZKpcLMmTNdHQoYhoFWq0VYWBh8fX259GQ+BMYeVCoViouLMXPmTMTFxWHq1KlQKBSora11STydYRgG//jHP/Daa69hwoQJeO211/D222/3+OHYUwoLC9HR0YFly5YhIyMDq1atwk8//cTVqvABO/VkMBh4OyYLK1pCwWw2o7KyEpGRkT1ewxo8eLDdInArfvvtN4wdO9buz2dkZGDv3r08RnSNy5cv49577+3RMSoqKrj6Jb4wm83Q6XQYMGBAj48lWHFhGAaffPIJHnzwQUHk4et0OohEIq5nS1EUQkNDXeIuwDAMjhw5gmHDhnFFiF5eXpg6dSpOnTrl8of40aNHIRaLuZt69OjRMBqNaG1tdVlMDMNg+/btWLFiBfcbDhgwAAkJCdi+fTtv56EoCoGBgdDpdLz+Dmxqs1CgaRpVVVUIDAy0el3iVkycOBENDQ08RXcNNu06IyPD7mPcfffdqKqq4rXtaZoGwzA9LmxMTk5GcXExr7GVlJQgIiKCl2eu65/a3VBbWwutViuYfRTUavVNGWQURblEXBQKBfR6PdLS0q77e9++feHt7Y3Kykqnx8TCMAw++ugj/PWvf+UeOBRFYdasWfjXv/7lsri0Wi1MJhNSUlK4v1EUhYcffhgFBQUwGo28ncvLywsURfE6IjIYDIKpZWIYBtXV1fDy8kJsbCwvacvsmiWfD0qLxQIAPXpQsve32WzmJSbg2ghaIpH0uN0iIyO5nUv5wGKxQKFQ8OaMIEhxYUct999/vyDy7dkLvqt1AlfE9/vvvyMzM/Omc1MUhalTp+LcuXMu6+UqFAoYDAYMGzbsur8/9dRTKCoqcllcP//8M1JTU29qM4lEgpSUFGzdupW3c1EUhYCAAGg0Gt6+r9lsFkQNBcMwqK2thcViuc4Sp6ewazh8TvMUFBT0uGaHoihERETg5MmTvMV14MABzJ49u8fHoSgKycnJKCkp4eU6Ky0t5dV/TpDiUl1dDbVajTvvvNPVoQC41utlF9Fdjdlshkaj6TZnPSoqCl5eXqiurnZyZNd49913MWnSpC4f4oBr1g0YhkFRURHuu+++Lv+/YsUKFBcXQ6/X83ZOtiPCp5i6uniQpmnU1tbCaDQiISGB9+nq+Ph4nD59mrfjnT9/HpMmTerxcRYsWMCbuLBrtz2ZqutMREQELBYLdDpdj45D0zQ6Ojp4tYkRnLgIba0FuJb+KZRK+NzcXERGRnbbNuzo5cyZM6Bp2qmxMQyD3NxcPP/8813GlZmZiS+//NKpMQH/Nz3SnUmmr68vhg4dik2bNvEmBmyRpFqt7vGxhLDWYrFYUFNTA5PJhISEBIcI3cSJE1FRUcHLsRiGgcFg4GUnxri4OK4uqad0dHRYVQtlLRRFIS4uDsXFxT06DlugzadzhDCe3p04c+YMzGazYNZa2AtKCPPdDMOgoqLitnVCffr0QVBQEM6dO+ekyK7R1tYGiqK6zRx6/vnncfToUafGBFwr0rudR9zSpUtRWVmJ0tJS3s7r7+8Pi8XCq2A5G/Yhza7jDRw40GEjqPDwcG6xu6ewHSs+2oxNy+cjE3PPnj0YPnx4j4/Tmfj4eOj1ers7kwzDoLW1lfcKfkGJi0ajwaZNm/Dss88KYgoK+L+FPEfFY8uNpFKpQFHUbQs2KYrC9OnTnT5H/+67795yn/GYmBiuktuZHDx48LZpnz4+Pli6dCkOHDjA23nZdYSepiXzuZhsC2y2VWVlJQICAhAfH+/QqTn2uuHj+5aWlvKyaM4yefJk7Nmzp0fHYNerZs2axUtMLGyGor2jvvr6eof43QlGXCwWC9avX4+xY8ciKSnJ1eFwqFQqh3oF5eXlWS0wOTk5XS5Kd4Wfn1+Pe0i2CB/DMLh8+TL++Mc/dvseiqLg7++P8+fP9yguW2AYpsvMuq7IyMjA448/zuv5+UhLZjf8ciY0TaO5uRn19fXo27cv+vXr55Rp6sDAQBQVFfX4OKdPn+Z1h9tJkyaho6Ojx78jAId0+lJTU9Hc3GxzfGzmX1paGu8daEGIi8ViwZdffgmRSISHH35YMKMW1oPKkTs6Xr16FR0dHVbFolAokJmZafWxe9qOO3bssPpiVSqVXA/qVqxcuRIff/xxj+KyBfaGtubByIofn7A9/Z6M1sxms9NS3hmGgU6nQ2VlJTQaDQYOHOjU/YzGjx+P3NzcHh2DXTRPTU3lKaprCRo9zWbbt28fEhISHNKWYrEYFEXZvMan0Wgcct0DAhAXi8WCDRs2oLm5GevWrXN5Rkxn2AerI2+sYcOG4fjx47d9X0tLCy/2JLbw1VdfQavVWvXejz/+GKNGjbptW82dOxdtbW1OW6Q+evSoSx10KYqCr69vjxf2nTFqoGka7e3tqK6uRkBAABISEuDn5+fUzl5ycjIvmU8A/202dOhQu6fGWB/AhQsX8hoTC0VRGDBgAEpKSmz6XElJCeLj4x3yG7tUXGiaxldffYWmpia8/PLLgrOqZh2VHXlzDR482Kppk5MnTzp91860tDT897//ve37GIbByZMn8cILL9z2vT4+PqAoymnV+qdOncKiRYuccq7ukEgkdi9UO0uETSYTampqIJPJ0L9/f/Tt29cl2ZrsOdkMP3soKytziCjOmTMHlZWVdv0mGo0GABy61UNMTAy3d5A10DQNg8Fgk1uyLbhMXBiGwaZNm1BfX48XX3zRoVNP9qLT6RyegiwSieDt7X1L6wt23cDZa1EvvvgiDh06dNv3abVam+wspk2bhnfffben4d0WdlozPj7e4ee6FWy2EfuAsQU+s566Q6/Xo6KiAt7e3khISEBAQIDLpqbZhBWpVGr3MU6dOsXregsLK1gymczmz+7atcsh6xqdYUfJ9fX1Vr2/uroa/v7+DovJJeLCMAwOHTqEK1eu4OWXXxaksLA3tTOmoUaNGoWzZ892+/+Kigr4+vo6vSfJZnfdrrjw008/7dIxoDv+9Kc/OWUNQS6X81pT0BMCAwO5jcJsQa/XO3TXSjbNOCwsDLGxsYLYIXPSpEl2Fy0yDHPLIuOeQFEUxo0bhx9//NHmmCoqKnpsVGkNqampqKmpue3ohWEYNDQ08LoudSMuueuKi4uxZ88erFu3zuk7AlqLSqXipnAcTUJCAvR6fbcXxIULFzBhwgSHx3EjFEUhKSkJGzdu7PY9DMPg6NGjePnll60+rr+/P/7+97/zEOGt2bNnj1VZYs6gc1GlLdMqRqPRYdPFNE2jsrISERERvJhP8kVKSordGXZs2rejOoXTp09Hc3OzTdN2V65cgUQicUrGX0BAABiGua1Xnlqtdrg3otPFpbm5GZ999hlWrVrlsLm+nsIWjjlrq2N2H4X29vab/sfuWhgdHe2UWG7kL3/5C/bu3dvtjd7W1gYANm0wRVGUU0aExcXFWLBggcPPYy3+/v7cSJBhGO7VHez/HNFWDMOgpqYGfn5+ghIWAJz7uD0uyTk5OQ59rnh7eyMqKgqHDx+26v0MwyA7OxsPPPCAU9qYoij07dv3lgv7DMOgpKQEAwcOdGhMThUXhUKBd999FzNnznT64rS1sIVjrLOtsxg6dChOnTp1098vXLiAiIgIl938MTExYBgGzc3NXf7/zTffxJw5c5wanzU9WtaRWCi2PQA49wKDwQC1Wg2dTgedTgeDwXDL7+SIttVoNNBqtQ7LFOopU6dOxYEDB2yutSotLcWMGTMcGBmwfPlynD171qpiz+LiYohEIl72R7GWxMREqNXqbqdgTSYTjEajwzusThEX9uH09ttvY9iwYbj33nud/jCyNluH3SzHmbn9wLXMrBunTBiGQXl5uV3bO/MFRVFYsGBBl9NYJpMJpaWleOqpp5wa06FDh257Yx84cADR0dGCe3B6eXndtF+8Xq/vcrpMp9M5dNQSFxcniPWorkhLSwNN07hw4QJkMhmqq6tRXFx8y0JG1nr+drVWPSU4OBhxcXHYvXv3LZ8pFosFO3fudNqohUUkEsHf3x9VVVU3/Y9hGBQXF6NPnz4Oj8nhV5bJZMKZM2fwzjvvYPjw4Vi+fLnTb3i9Xg+ZTAaFQtHtQ4mdp5TL5QgKCnJ6vY2Xlxe8vb2vy/Sora2Fj4+Py1O0V69ejcrKypsKyD755BOkpKQ4vXq8sLAQGzduRGtra5c3N5savWLFCqfGZS0ikQi+vr6QSCSQSCQICgriCv/Y78NOzfKd7MIu5Pr6+gp2vRO41qlZtGgRpFIpsrOzcerUKVy9ehW7du3ChQsXbvrd2emnkSNHOvz5QlEUli9fjuLiYpSXl3d7De7atQt9+/blxTzTVtLS0tDY2HjT6IXtyDgj89Qh4sJW+V64cAEffvgh9u3bhwcffBD333+/S3pKarUagYGB8PLygkwmu25XP3ZUo1aroVAoEBAQ4JINwABgwoQJOH36NBfT6dOnMXnyZJf3vn18fDB9+nS89tprXLs1Njbi0KFDeOutt5wez9NPP42wsDB88cUXOHToEGQy2XW/5/nz5+Hr64uIiAinx2YtnfehF4lECAwMhNFo5K5N9vvwfb9otVrI5XJe92JxFJGRkViyZAkWLFiAJUuWYP78+ZgzZw4KCgpw5MiR6zqK9fX1UCgUGDdunFNi8/Pzw3333YcffvgB1dXVN804nDx5EuXl5XjooYdc0s5isRjBwcG4evUqFxtN0ygoKEB8fLxTnsO85R1evHgRkZGR0Gg0uHr1Ki5fvgyapjFhwgRMmjQJgYGBLruYw8LC4OXlBbFYDJFIBLlcjsDAQHh7e8NkMnFbGIeGhjq8aPJWxMXFgWEYlJWVob29HQEBAS6tLu/M2rVrsXTpUnz//fcYOXIk/vnPf+LBBx9EaGio02ORSCRYvHgxKisrcezYMVy4cAEZGRnIyMiAWq3Grl278NRTTwn+4dkZVmDYjpBOp+MsPfhCo9GgurpaMCnH1iAWi68bGUdHR+P+++9HdnY29uzZg3HjxsFkMuHgwYOYMWOGUzuvqampmDVrFn744QeMHj0agwcPhtlsxsWLF1FZWYlHHnnEZR1ViqIwZMgQ5Obmora2FmFhYaiuroZYLEZcXJxTYuDtCvvll19gMBjg5eWFmJgYzJs3D6mpqdd51rhqX4rOU1z+/v7w8vLipiDY+cnOF4Ez47zxXNOmTcPp06chFou5hUlXtVvn83p7e2P9+vVYv349fv/9d0yfPh0PP/ywS2JjGAYURSExMREDBgxAdXU1zp49i59//hkikQiLFy9GfHy8y2KzF29vb/j7+3Ob0/n7+/P6Herq6tC3b1+EhIQIYo+YztgSj7+/PxYtWoRz587h999/B3BtL5iUlBTev9ftjjd69Gj069cPJ0+eRHFxMbe/yqpVqxzezrc7tpeXFzIyMlBeXo7W1lYEBQVx02HO+P15EZfAwEBkZmZy+3z7+vqCoihe98awV21FItFNOd+sURv7kKIoqkd7qNvbC/T19UVdXd1Nf09LS4OXlxcvFilhYWF2fS44OLjL7LWFCxdCr9cjJCSkx7sG2jPvGxAQgMLCwpv+npGRgUGDBsHLywu+vr5dvsdaYmJi7PqcSCTistTsha09oCiqy2PZuxbo7e2NiIgI+Pj4OGw3UHt76RKJxC67+OjoaISHh3M1RLc6hi2p8iz+/v5We3VlZmZCr9dzv19jYyMaGxtv+zl7Zya8vb2tMrwFrrWTxWKBj48P5HK51efo6XofxfAgYT3xAbIWeyutndVDs2f6wln7mtjTbs74TQHbH5bkWrPvWhNybEK9D4QaFyDs35P7LB/iYgsajQYVFRVITk522Xxkd+h0OlgsFoenMtoDu0+2RCIRlHM0TdMoLy9HdHS04NpNLpejuroa6enpgmoz4Frlvdls5nVDKz5gGAZtbW3w9fUVVI0Qi8VigVar5aa3hYJGo0FZWRlSU1Odvknf7Whra3OoQWV3OD11q6WlBVu2bMErr7yCixcvOvv0t0Wj0fR450BHoFAosGfPHi6XXyh8+eWXeOGFF+wy83MUNE3j0KFD+Ne//oXTp0/32MLdEbCp7yqVymmjRGtgp4jr6+t7PMXnCDo6OvDdd99ZPSXkDCwWCzZv3owTJ04Iqm7IbDajuLgYJSUlt7SXchROb4mEhAS8/vrrSE1NxRdffIHvv/++R+sdfCKRSODr6wulUun0rXjdkYsXL2L37t1YtWoV+vfv7+pwAAAymQyff/45jh49ipkzZ+KJJ54Q3IgKwHV1JkqlUlAdmn79+sHLy8tqd93ezu+//47m5mYsWrTouuJYV6JQKHDx4kUoFAoMGTIESUlJTh8huyQf0d/fH08++SROnjyJbdu2QSqV4oknnnBaitytCA4ORnt7O5RKpUvSbN0FtVqN9evXY8SIEYLx77p8+TJ27NgBiUSCp59+2qmWG/bg5eWFoKAg6HQ6aLVamEwml9rdd44rNjYWVVVVaG9vF3S9kKupq6tDTk4O7rzzTrsTQfiEdV+ora1FSEgIBg8e7PQiZxaXJbtTFIXJkycjKSkJX331Ff75z39iyZIlmDZtmktvLpFIhODgYMjlcm6Ng3Az//nPf6DT6bBu3TqXPwyNRiN2796N3NxcDBs2DIsXL3ab343NXPTx8YFGo4FSqURAQIDL61ACAgIQERGB5uZmBAYGCm4dQQgYjUbs3LkTsbGxLrVoYtHr9bh69SrUajUGDhyI2NhY1z5LXXbm/yU6Ohqvvvoq7rzzTvzwww/4z3/+47BUSWthrTmENh8uFI4fP45jx47hmWeeQVRUlEtjqa+vx0cffYQrV67ggQcewLJly9xGWDrj4+OD4OBgiEQiqFQqQawT9e3bF2KxGHV1dYKrixEChw8fhkqlwqJFi1y+1tLa2opLly7BZDIhMzMTcXFxLu/0uVxcgGs31gMPPIBnn30WVVVVeOONN1BUVOTSmIKCgiASiQS3gO5q2tvb8dFHH2Hq1Km46667XBYHwzA4fvw4/vOf/0AsFuO5557D6NGjXX5D9QSRSISgoCBIJBLo9XqoVCqXrv2xBYEGgwEtLS0ui0OIlJWV4fz585g1a5ZLpw0tFgtKS0tx9epVhIeHY8SIEYLxjBOEuLBkZGTgb3/7G+Li4vDhhx/i559/tsrW2hFQFIWQkBCYTCa7tqf1RBiGwfvvvw+xWIxnn33WZQ9ylUqFr7/+GtnZ2Zg0aZIgRlB84ufnh6CgINA0DaVS6dKEFz8/P/Tp0wdtbW3QarUui0NIaLVa7NmzB4MGDcLo0aNdFodarcalS5fQ3t6OlJQUDB48WFDp2YIzGAoODsZzzz2Hw4cPY9euXbh69Soef/xx9OnTx+mx+Pj4ICAgAGq1Gr6+vi6fB3c1+/btQ25uLv7f//t/LquBKCkp4baZXb16NVJSUlwSh6Px9vZGcHAwtFotNBoNTCaTQ/c7vxURERFQqVSor69HUlKSy6eAXAnDMNi3bx/MZjMWLFjgsg5WXV0dqqurERAQgPT0dMHVDAICG7mwUBSFWbNm4ZVXXoFOp8Nbb72FU6dOuWTel11cVSgUvXreua6uDv/9738xb948l/TWzGYzsrKy8M033yAuLg4vvPCCxwoLC0VRCAgIQEBAAEwmE5RKpUtG8hRFITY2FmazGU1NTU4/v5DIz89HYWEh5s2b55LpJ6PRiIKCAlRVVSE2NhbDhg0TpLAAAhy5dGbAgAH461//iu3bt+Pbb79FYWEhVqxY4dQFW3Z6rKOjA2q1WjDzmc7EYrHgnXfeQWRkJB5//HGnn7+lpQVbt25Fc3Mz7r33XkyaNMmt11ZsRSwWw9vbGxqNBiqVChKJxOkPFLFYjH79+qGhoQFBQUG98j5QKBTYv38/MjIyMHToUKefv6OjA1KpFBRFIT09XfClEoIcuXTG19cXK1euxOOPP478/Hy8+eabdpnc9QRvb28EBARAq9UKpuDTmWzfvh2lpaV46aWXnPpQYxgG586dw0cffQSTyYRnn31WEPvbuAJ2sd/Pzw86nc4li/1hYWEICgpCQ0ODy9ZCXQXDMNizZw/EYjHmzJnj1HPTNI2KigoUFRUhKCgII0aMELywAG4gLixjxozB3/72N4SEhOCdd97Bvn37nHpzBQQEQCwWQ6lU9qrpMalUii1btmDp0qUYMmSI086r0+mwefNm/Pzzzxg5ciSee+45QRSpuRp250p2sd/ZFi0xMTFgGMYqx19P4ty5c6ioqMDChQudOnOi1Wpx+fJlNDU1ISkpCWlpaYJxAbgdgp4Wu5GIiAi8/PLLyMrKwt69e1FcXIxVq1bZbStvK2z1vkqlEqSpH98YDAa8/fbbSEhIwPLly5123qqqKmzduhUGgwEPPfQQMjIynHZud4Bd7NdoNFyyibMMML29vRETE4Pa2lrI5XK36EH3lNbWVhw+fBjjxo1z6pbFTU1NqKiogJ+fH4YNG8b7lteOxq3EBbg2PbBgwQKkpaVhw4YNeOONN7By5UqMGDHC4edm7TqUSiV8fX09vmp548aNaG5uxqeffuqUTDmapnHkyBH8+uuvGDhwIJYuXdorHl72QFEUAgMDYTAYoNPpYDabERAQ4JRU1ODgYISGhqKxsREBAQFu05O2B4vFgl27diE0NJTbvM/RmM1mSKVStLe3o1+/fkhMTHTLDD33i/h/SU5O5gwwP//8c2zevNkp6yG9xdzy0qVL2LVrFx577DHEx8c7/HwymQxffPEFfv31V8ycORNPPvkkERYr6GyAqVKpnGaA2VvMLY8fP46mpiYsXrzYKSKqUChw6dIlznBy0KBBbiksgBuOXDoTEBCAJ598Ejk5Ofjhhx8glUrx+OOPO9wA09PNLdVqNd577z2MGDECCxcudPj5rly5gp9//hl+fn54+umnMXDgQIef05NwhQFmbzC3ZE0p77jjDoev991oOJmSkuL2MyPuKYmdoCgKU6dOxWuvvQYvLy/885//xNGjRx266M6aW7JTEp7Gp59+6hRTSqPRiJ9//hmbN2/G4MGDsXbtWiIsdsIaYAYGBsJsNjulJqazuaWQtgzgA6PRiF27diE6OtrhppR6vR5XrlxBXV0dBgwYgPT0dLcXFsADxIWFNcCcOnUqtm/fjk8//dShBpieam55/PhxHD16FH/6058caqnCGk5eunQJ999/v9saTgoNZxtgeqq55eHDh6FUKrF48WKHTkvdaDjZv39/j0m19xhxAa7dWA8++CCeffZZVFRU4M0330RxcbHDzudp5pYdHR34+OOPMWXKFEybNs0h52AYBjk5OZzh5PPPP48xY8Z4zA0lBJxpgNnZ3LK1tdUh53A2rCnlzJkzHTbdZ7FYIJVKOcPJ4cOHe1xhqkeJCwtrgBkTE4MPP/wQO3bscMgUAUVRCA4O9ghzS9aU0tvbG2vWrHHIw16tVuObb75BVlYWJk2a5PDRUW/HWQaYfn5+iIqKQmtrq9ubW+p0OuzZswdJSUkYM2aMQ86hVquRl5eHtrY2znDSE30LPe8b/S8hISF4/vnncejQIezatQslJSUOMcAUi8UICAiARqNxa3PL/fv34/z58/jHP/7hkBqe0tJSbN++HQCwatUqDB48mPdzEG7GWQaYkZGRUKvVbm9u6WhTyvr6elRVVSEgIADDhw/36Klg97wCrISiKMyePRuvvvoqZ4B5+vRp3ueG2foCdzW3rK+vx5dffom5c+fy3lszm83Izs7Ghg0bEBsbixdeeIEIi5NxhgGmJ5hb5ufno6CgAHPnzuW9g8UaTlZWVnKGk54sLIAHj1w6M2DAALz22mvYtm0bNm7cyBlg8uWT1dncUqPRIDAwkJfjOgPWlDIiIgJPPPEEr8dubW3F1q1b0dTUhPnz5/daXzCh4GgDTHc2t1Qqldi3bx8yMjKQnp7O67FlMhlKS0vdxnCSLzx65NIZPz8/PProo1i9ejWuXLnCuwEma26p0Wjcytzyhx9+wNWrV/Hyyy/z9qBhGAbnz5/Hhx9+CKPRiGeeeQZTpkwhwiIAHG2AGRYWhsDAQDQ0NLhNFiXDMNi9ezfvppSs4WRhYaFbGU7yRa8RF5axY8fi9ddfR3BwMN555x3s37+ft5vL3cwtpVIpNm/ejAcffJA3U0qdToetW7fip59+wogRI/Dcc88hNjaWl2MT+MORBpixsbFgGAYNDQ28HdORsKaUCxYs4G2qijWcbGxsRGJiolsZTvJFr5gWu5HIyEi89NJLyMrKwp49ezgDTD56Fe5ibmkwGPDOO+8gISEBK1as4OWYVVVV2LZtG3Q6HZYvX45hw4bxclyCY3CUAaY7mVu2tbXh8OHDGDt2LJKSkng5ZmfDyeHDh7ud4SRf9LqRC4uXlxcWLlyIF154Ac3NzXjjjTeQl5fHy3FZKw4hVy1v3LgRjY2N+POf/9zjDDeapvHrr7/i888/R0hICNauXUuExU1gDTD9/f1hMBh4KwrubG7p7G0BrMVisWDnzp0IDQ3FzJkze3w8s9mMkpISlJWVoU+fPr1aWIBeLC4sgwcPxt/+9jckJyfjs88+w5YtW3p8Mwjd3DIvLw+7du3CqlWremxKKZfL8eWXX+Lw4cOYMWMGnnrqKadtgUDgD19fX26kzZcBptDNLXNyctDU1IRFixb1eMpKqVTi0qVLkMvlbm84yRe9clrsRgICAvD000/j+PHj+PHHHzkDzJ6sFQjV3JI1pRw+fHiPTSnz8/Px888/w9fXF0899RQSEhL4CZLgEvg2wBSyuWV9fT2OHz+OqVOn9ug+90TDSb7o3dLaCYqicMcdd+Avf/kLKIrC//t//w/Hjh2ze2FeqOaWn332GTQaTY9MKY1GI3bs2IHvv/8egwYNwtq1a4mweAh8G2AK0dzSZDJh586dPTal1Ov1yM/P9zjDSb4g4nIDMTEx+J//+R9MmTIF27Ztw2effQa1Wm3XsYRmbpmTk4MjR47gmWeesdupoKGhAR9//DEuXryI++67DytWrPD4YrDeCJ8GmH369BGUuSVrSrlo0SK7N1dra2tDXl4eDAYDMjIyPMpwki+IuHSBj48Pli5dij/96U8oKyvDG2+8gZKSEruOxZpbKpVKnqO0jY6ODnz00UeYPHmyXaaUrOHkJ598Am9vbzz33HMYO3YsuaE8GL4MMEUikWDMLcvLy3Hu3DnMnDkTkZGRNn+eNZwsKSlBaGgoRowYIeisUFdCxOUWDBs2DH/7298QHR2NDz74ADt37rR5BMKaWxqNRpeZW/bUlFKtVmPjxo3IysrCxIkTezTyIbgffBhgCsHcUqfTYffu3XabUnY2nExOTkZqaqrbegk6A9IytyE0NBRr167FwYMHsXv3bs4A0xY3X7FYDH9/f5eZW7KmlG+99RZCQkJs+ixrOMkwDB577DGkpqY6KEqCkOHDADMyMhIqlcpl5pb79u2DyWSyy5SyNxlO8gUZuVgBRVG4++678ec//xkajQZvvvkmzpw5Y9MxAgMDXWJu2dDQwJlSjh071urPWSwWznAyJiYGL7zwAhGWXk5XBpi2jOTZvV/MZjOam5sdGOnNFBQUoKCgAPPmzbNpGquz4WRMTEyvMJzkCzJysYGEhAT89a9/xbZt2/DNN9+gsLAQy5cvt8qTizW3bG9vd5q5JWtKGR4ejscff9zqz3U2nJw3bx7xBSNcB2uAqVaroVQqbTLAFIvF6Nu3LxobGxEUFOSU+0CpVCI7Oxvp6ek2mVKyhpMAepXhJF8QcbER1gBz6NCh2Lx5MyoqKrB69WqrUnG9vb0RGBgItVoNsVgMsVjs0Fh//PFHlJSU4IMPPrCqt8UwDC5cuIDdu3cjJCQEzzzzDPEFI3QJm2qv0+mg0+lgNpvh7+9v1VRXeHg4Nz02aNAguzO2rIFhGOzZswc+Pj6YO3euVZ+haRpVVVVoaGhAWFgYUlJSep0vGB+QaTE7GTt2LP76178iMDAQb7/9Nn755RerMmkCAgLg4+PjcHPLsrIyfP/991abUup0Omzbtg0//vgjMjMzieEkwSokEgkCAwNhsVhsMsB0lrnl+fPnUV5ejoULF1rVwdLpdNcZTg4dOpQIi52QkUsPiIqKwssvv4y9e/di9+7dKCoqssoAk50ec5S5pdFoxNtvv221KWV1dTW2bt1KDCcJdsHWxNhigOkMc0tbTSlZw0lfX99e7wvGB2Tk0kO8vLywaNEirF27ljPAvHz58m0/40hzS9aU8uWXX75lZlpnw8ng4GBiOEmwG3sMMIODgxESEoKmpibezS0tFgt27dqF4ODg25pSEsNJx0DEhSdSU1M5A8xPP/0UW7duveUN4yhzy8uXL2Pnzp149NFHMWDAgG7fJ5fL8d///heHDx/GtGnT8PTTTxPDSUKPsdUAMzo6GiKRiHdzy5ycHDQ2NmLx4sW3nNbqbDiZmprq8DWg3gSZFuMR1gDz999/x08//QSpVIrVq1d3u3bBt7mlRqPBu+++i2HDhmHx4sXdvq+goAA//fQTxGIxnnzySSQmJvb43AQCiy0GmI4wt7TGlJJhGNTW1qKmpgbBwcEYPHgw8QXjGTJy4RmKonDnnXfif/7nfwAA//znP/Hbb791uXjPt7kla0r54osvdnkjm0wm7NixA5s2bUJSUhLWrl1LhIXgEGwxwOTT3NJkMmHXrl3o169ft6aUBoMB+fn5qKmpQXx8PDIyMoiwOAAiLg4iNjYW//M//4PJkydj69at+Pzzz7u0f+HL3PLEiRP49ddf8ac//alLa5bGxkZ89NFHuHjxIpYsWYKHHnoI/v7+dp+PQLAGaw0w+TK3PHz4MORyORYvXtzl9FZbWxsuXboEg8GAzMxMxMfHkxouB0HExYF0NsCUSqV44403cPXq1Zve11NzS9aUctKkSZg+ffp1/2MYBidOnMAnn3wCLy8vPPfccxg3bhy5oQhOwxoDTJFIhNjY2B6ZW97KlJIYTjofIi5OgDXA7Nu3L95//33s2rXrulFKZ3NLW039GIbBBx98wAlHZ9HQaDT49ttvsXfvXowfPx7PPvssMZwkuIzbGWBKJBLO3NLWaWKdToc9e/YgMTHxJpsj1nCytbWVGE46EdLCToI1wDx06BBngLl69WrOAJM1t2Sr9629+H/55RecO3fuJlNKqVSK7du3g6ZpPProo1YVUhIIjuZ2BpisuWVdXZ1N5pb79++H0WjEwoULr+tgdTacHDFiBPEFcyJk5OJERCIRZ4CpVqvx1ltv4ezZs9z/bTW3bGxsxJdffol77rmH661ZLBbs27cPX331Ffr164e1a9cSYSEIilsZYNpjbllQUID8/HzMnTuXm+oymUwoLCzkDCczMzOJsDgZIi4ugDXAHD58OL7++mt888030Ov1nLml2Wy+bvGfYRi0t7ejtbUV7e3tYBgGNE3jnXfeQVhYGJ588kkA1xYrP/30U5w4cQJz587F6tWrybwyQbCIxWIEBQWBoigolUro9Xru73379kVHR8d1u8Cy9wH7YhgGSqUS+/btu86UUiaT4eLFi1Cr1Rg6dCgSEhKcbu9PAChGCPuO9mLOnDmDLVu2IDg4GI8//jgGDhzI2WiIRCJs3boVn3zyCcrLy7nPJCUlYdKkSaivr8fHH3+MIUOG4OLFi1xF8rJlyxAXF+fCb0Ug2IZOp4Ner4ePjw9ngFldXQ29Xo/IyEhs3rz5pvsgMTEREyZMQGpqKtatWwdfX19UV1ejvr6eGE4KACIuAqC1tRUbNmxAdXU1Fi5ciNmzZ2PHjh1YuXIltFotKIrqcppMLBbj559/hkqlQl5eHkaPHo2FCxc63G2ZQHAEJpMJWq0WDMNwRZfffvst1qxZw41quroPJBIJtm/fjvj4eGg0GgwcOJCYrgoAIi4CwWKxYM+ePTh48CAYhsGGDRsAdH0zdYaiKCxduhQvvfQShg8f7oRICQTHwTAMt9B//PhxLF68GAzD3PI+oCgKFEXho48+wiOPPOKUPWIIt4eIi8A4d+4cJk+ebLWRH0VRkEgkqK+vJ5sZETyG5uZmJCYmQqfTWZXcQu4D4UFWuQTG6dOnbXKIZRgGOp0OmzZtcmBUBIJz2b59OzdFZg3kPhAeZOQiIBiGQXJyMioqKmyywKAoComJiZBKpaTynuD2kPvAMyDiIiDa2tq4okp7P8+HqyyB4ErIfeAZkGkxAdE5p98eVCoVT5EQCK6D3AeeAREXAdHTLJegoCCeIiEQXAe5DzwDIi4CIiIiAklJSTbPF1MUhaSkJISHhzsoMgLBeZD7wDMg4iIgKIrCs88+a9dn16xZQxYxCR4BuQ88A7KgLzDkcjni4uKg0+lu2vOiK0QiESQSCerq6kh+P8FjIPeB+0NGLgIjNDQUO3bsAEVRtzXbE4lEoCgKO3fuJDcUwaMg94H7Q8RFgMyePRv79u2DRCLhrC06w/5NIpFg//79mDVrlosiJRAcB7kP3BsiLgJl9uzZqKurw4cffojExMTr/peYmIgPP/wQ9fX15IYieDTkPnBfyJqLG8AwDDo6OqBSqRAUFITw8HCyaEnodZD7wL0g4kIgEAgE3iHTYgQCgUDgHSIuBAKBQOAdIi4EAoFA4B0iLgQCgUDgHSIuBAKBQOAdIi4EAoFA4B0iLgQCgUDgHSIuBAKBQOAdIi4EAoFA4B0iLgQCgUDgHSIuBAKBQOAdIi4EAoFA4B0iLgQCgUDgHSIuBAKBQOCd/w/+mxHOIc9MKAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train the model\n",
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.00);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d92f84a5",
   "metadata": {},
   "source": [
    "$\\lambda=10^{-2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f1a96caf",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 6.01e-01 | test loss: 5.65e-01 | reg: 1.78e+01 : 100%|██| 20/20 [00:13<00:00,  1.51it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train the model\n",
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.1, lamb_entropy=10.);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae826b35",
   "metadata": {},
   "source": [
    "$\\lambda=1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0da2ead7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 1.09e+00 | test loss: 1.02e+00 | reg: 5.18e+00 : 100%|██| 20/20 [00:11<00:00,  1.67it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train the model\n",
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=1);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "650e7432",
   "metadata": {},
   "source": [
    "### Parameter 2: (relative) penalty strength of entropy $\\lambda_{\\rm ent}$.\n",
    "\n",
    "The absolute magnitude is $\\lambda\\lambda_{\\rm ent}$. Previously we set $\\lambda=0.1$ and $\\lambda_{\\rm ent}=10.0$. Below we fix $\\lambda=0.1$ and vary $\\lambda_{\\rm ent}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0d92d91",
   "metadata": {},
   "source": [
    "$\\lambda_{\\rm ent}=0.0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d57d3cee",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 8.90e-02 | test loss: 8.40e-02 | reg: 1.68e+00 : 100%|██| 20/20 [00:12<00:00,  1.65it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train the model\n",
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.1, lamb_entropy=0.0);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25d3f9f1",
   "metadata": {},
   "source": [
    "$\\lambda_{\\rm ent}=10.$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "94450fdf",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 6.03e-01 | test loss: 5.67e-01 | reg: 1.77e+01 : 100%|██| 20/20 [00:10<00:00,  1.89it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.1, lamb_entropy=10.0);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cb475c3",
   "metadata": {},
   "source": [
    "$\\lambda_{\\rm ent}=100.$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5370c135",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 1.60e+00 | test loss: 1.54e+00 | reg: 2.69e+02 : 100%|██| 20/20 [00:11<00:00,  1.67it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.1, lamb_entropy=100.0);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "409bfc64",
   "metadata": {},
   "source": [
    "### Parameter 3: Grid size $G$. \n",
    "\n",
    "Previously we set $G=5$, we vary $G$ below."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c841825",
   "metadata": {},
   "source": [
    "$G=1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c78702b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 1.41e-01 | test loss: 1.33e-01 | reg: 1.01e+01 : 100%|██| 20/20 [00:06<00:00,  2.95it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=1, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.01, lamb_entropy=2.);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e678b38",
   "metadata": {},
   "source": [
    "$G=3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9b649166",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 6.18e-02 | test loss: 5.66e-02 | reg: 5.93e+00 : 100%|██| 20/20 [00:11<00:00,  1.76it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7u/umr0VElE+SJMFoNCr+x2AwYOPGjdi5c6fa/8VpNBsusyWEQHd3N9rb22G329HR0YFIJIJgMKh2aUREOTM8PIxLly7hjTfeULuUaQomXHw+HyRJQk1NDYBr3xLa29tx/vz5WV0gQESkJ0899RT+5m/+RnOtq7RVzRwJIdDb24tly5ZNm/Kqrq5GOp1GMplUsToioty4evUqzp8/j3/8x39Uu5SfKIhwSSQSEEL8pJOxJEmora1FT0+PSpUREeXOhg0b8Jd/+Zea3NenyavFZiuzu/VGC/Wtra349ttvs9eNExEVgrGxMfzwww/49ttv1S7lhnR/5iKEQDQaRXNz8w3/PTMPGY1G81kWEVFObdiwAb/85S81249Mm1XNgt/vz16OdzMNDQ3o6enJ6QYmIqJ8GR4exg8//IATJ06oXcpN6f7Mpa+vD21tbbd8TGNjI2KxGK8aIyLdE0LgiSeewN/+7d9q9qwF0Hm4CCGQTqfhcDhu+bjMWQ2vGiMivTt+/DgGBwfxD//wD2qXcku6DpfLly/DbDbPaKHe4XCgr68vD1UREeWGLMvYuHEj3nrrLc3ta7metqu7BSEEhoeHsWzZshk9vrW1FRMTEzmuiogod/7u7/4O1dXVePnll9Uu5ba0O2F3G7IsQwgx4+7JmbnJmXRMJiLSmt7eXvzzP/8zBgcHdbGtQrefsn19faiqqprxIEuSBLPZjKtXr+a4MiIiZcViMTzyyCP4l3/5FzQ1NaldzozoMlyEEPD5fFi6dOmsntfW1oahoaEcVUVEpLxUKoUNGzZg9erV+Ou//mu1y5kxXU6LTU5OQpKkWV+GV1VVlZ1OIyLSung8jhdffBGhUAifffaZLqbDMnR35iKEQE9PD5YuXTrrgc48nrv1iUjLhBC4ePEi1q1bB5/Ph6NHj8JsNqtd1qxoNlxudnYRDodntLflZurr69Hb2zuf0oiIckIIgUgkgl//+td48MEHcdddd+Hzzz9HRUWF2qXNmmanxcbGxlBXVzft7CRzQ7C2trY5nx42NTXhwoULSpVJRDRvQghcvXoVBw8exH/+538inU7jv/7rv/Dss8/qaipsKs2Gy+DgIIxGY/bmX0IIDA0NwWg0ora2ds6vazAYsGzZMrbhJyLVZLqLXLlyBX/4wx9w8OBBHDt2DI2Njfirv/orPP/887o8W5lKs+GyYsUKnD17FgaDAZWVlfB6vRgdHcU999wzryTX67cAItK/q1ev4scff8SxY8dw7Ngx9PX1oa6uDhs2bMBrr72Gu+++W3drKzej2XCprKxEe3t7dsOQwWDAqlWrCmbgiaj4rF27FhaLBffddx+cTiceeughLFmyBKWlpQX3xVeT4WIwGBAIBGAwGNDY2IhUKgWz2YxEIoFEIqHIe5SWliryOkREM2E2m/Hnf/7naGtrQ0VFBSRJQm9vr6IXGC1ZskSx15ovSWhw04csy3l5H7aBIaJ8yccWCKPRqJnZHU2Gy2zIsox4PI7S0lKGBREVhKkfy3qdLtP9p3E0GsXp06e5MZKICsbJkydhMBhw8uRJtUuZM92HCxERaQ/DhYiIFMdwISIixTFciIhIcQwXIiJSHMOFiIgUx3AhIiLFMVyIiEhxDBciIlIcw4WIiBTHcCEiIsUxXIiISHEMFyIiUhzDhYiIFMdwISIixTFciIhIcQwXIiJSHMOFiIgUx3AhIiLFMVyIiEhxDBciIlIcw4WIiBTHcCEiIsUxXIiISHEMFyIiUhzDhYiIFMdwISIixTFciIhIcQwXIiJSHMOFiIgUx3AhIiLFMVyIiEhxDBciIlIcw4WIiBTHcCEiIsUxXIiISHEMFyIiUhzDhYiIFMdwISIixTFciIhIcQwXIiJSHMOFiIgUx3AhIiLFMVyIiEhxDBciIlIcw4WIiBTHcCEiIsWZ1C5gPoQQ8Hq9GBkZQX19PcrLyyFJktplaZoQAuPj4wiFQqisrERNTQ3HbAY4brPHMZsbIQT8fj8AwO/3Qwihz3ETOuT3+8Wbb74p2tvbBYDsn/b2dvHmm28Kv9+vdomawzGbG47b7HHM5qbQxk134XLkyBFRUVEhJEkSkiRN+yFk/q6iokIcOXJE7VI1g2M2Nxy32eOYzU0hjpuuwuXIkSPCaDQKg8EwbfCv/2MwGITRaNTVDyJXOGZzw3GbPY7Z3BTquElCCDHvubU8CAQCaGpqQjQahSzLt328wWCAxWLB8PAw7HZ77gvUII7Z3HDcZo9jNjeFPG66uVrsrbfeQiQSmdEPAABkWUYkEsHbb7+d48q0i2M2Nxy32eOYzU0hj5suzlyEEOjo6EBfXx9mU64kSWhra0NPT48+r7aYB47Z3HDcZo9jNjeFPm66CBev14u6urp5Pb+mpkbBirSPYzY3HLfZ45jNTaGPmy6mxUKh0LyeHwwGFapEPzhmc8Nxmz2O2dwU+rjpIlwqKyvn9Xyr1apQJfrBMZsbjtvsccxmL5lMIhqNzus1tD5uugiXmpoatLe3z3p+UZIktLe3o7q6OkeVaRfHbG44brPHMZuZeDyO0dFRnD17FqdOnUIoFEJzc/OsX0cv46aLcJEkCa+99tqcnvv6669retErVzhmc8Nxmz2O2c3FYjFcvnwZXV1dOH36NIaGhmAymdDa2orVq1fjjTfemNP/Xw/jposFfaCwrwfPFY7Z3HDcZo9j9n8ikQj8fj/8fj+i0SgMBgPsdjscDgdsNhuMRmP2sYU8bro4cwEAu92OvXv3QpKk2ya2wWCAJEn48MMPNf8DyKWpY2Yw3PpHzTH7Pxy32Sv2MQuFQhgaGsLp06fR1dWFq1evoqKiAh0dHVi9enV2GmtqsAAFPm75bgkwX0eOHBEWi+WG7RGm9uDp7OxUu1TNmGnfIo7ZdBy32SuWMZNlWUxMTIiBgQFx8uRJceLECXHy5EkxMDAgJiYmhCzLs3q9W41bZuz0Nm66CxchhPjggw/E9u3bRVtb20+6h+7atUsEAgG1S9Qcv98vdu3adcOOqxyzm+O4zV6hjlk6nRZ+v1/09fWJ77//Xpw4cUKcOnVKDA4OimAwOOtAud7Nxm3x4sXi3/7t33Q3brpZc8mQZRm7du3C3XffjXXr1sHn8yEYDMJqtaK6ulrzi1xqE0JwzOaA4zZ7hTBm6XQaExMT8Pv9CAQCkGUZFosFDocDDocD5eXlir/n1HGrqKhAMpmEzWZDRUWF4u+VS7oLl76+PuzevRt/8Rd/gfr6erXLIaICk0qlEAgE4Pf7MTExASEEysvLs4FisVjyWo/P54Msy6itrc3r+86X7u5E2dXVherqagYLESkmmUxmr/AKBoMQQqCyshLNzc2w2+0oLS1VrTaLxQK/3490Ov2TCwK0TFfhkk6nce7cOaxZs0btUohI5+LxeDZQQqEQJEmC1WpFS0sLHA4HSkpK1C4RAFBWVgZJkhCNRufdDSGfdBUuFy5cQDwex6pVq9QuhYh0KBqNZgMlEolAkiTYbDa0trbCbrfDZNLeR6IkSSgrK2O45FJXVxcWLlyou7lHIlJPOBzOBkosFstualy0aBHsdvtt95dogcVigc/nQyqV0mQA3og+qgSQSCTQ09ODn//852qXQkQaJoRAKBTKBkoikYDJZILdbkdzczOqqqp0EShTlZaWZqfGtN6wMkM34dLT04NUKoU77rhD7VKISGOEEJicnMxeMpxMJlFSUpK9wstqteruMuipJEmCxWJhuORCV1cXGhsbYbPZ1C6FiDRAluVpe1DS6TRKS0tRU1MDh8Ohq/WJmbBYLIhEItng1DpdhEs0GkVvby/Wr1+vdilEpKLMpkafz4eJiYnspsaFCxfmbFOjVpjNZhgMBkSjUYaLUs6dOwchBFauXKl2KUSUZ5lNjT6fD5OTkxBCoKKiAg0NDXA4HCgrK1O7xLyYOjVWVVWldjm3pYtw6erqwuLFiwvuNJeIbiyRSGR3yU9OTgK4dufF5uZmOBwOmM1mlStUh8ViQTgcRiKR0PwYaD5cQqEQBgcH8cwzz6hdChHl0I02NVZVVWHJkiWw2+26mArKNbPZDKPRiGg0ynCZr7Nnz0KSJCxfvlztUohIYddvajQYDLDZbGhra4PNZtPNno58yizsa/3iJs3/5Lq6utDe3p73ZnFElBvXb2o0Go2w2+1oaGiAzWbT3R6UfLNYLAiFQojH46r2PLsdTYfLxMQELl26hK1bt6pdChHN0c02NTocDrS0tKCqqkrXe1DyraSkBCaTCdFolOEyV2fOnIHJZEJHR4fapRDRLEzd1Oj3+5FKpWA2m2G321FdXY3KykoGyjxkFvaFEJodR02HS1dXFzo6OjS/cEVEN9/UWFdXB4fDobubXWmZxWJBMBhEPB7X7KXYmg2X8fFxjI6OspcYkYal0+lpN9Yqpk2NajKZTCgpKUE0GmW4zFZXVxdKS0vR3t6udilENEUymZy2B6VYNzWqLXP2otWpMU2Hy/Lly3kpIpEGJBKJaXdqBLipUW0WiwWTk5OIxWKavJpWk5/cV65cgc/nw4YNG9QuhahoxWKxbKCEw2FuatQYo9EIs9mMaDTKcJmprq4ulJeXY8mSJWqXQlRUIpFINlCi0Wh2U+PChQtht9t1dQ/3YpA5e5FlWXP7gzQXLkIInDlzBitXrtTcYBEVoql7UOLxeHZTY+YWFzwOtausrAwTExOIxWKau3hCc+Fy6dIlTE5O8qZgRDkihEAwGMxeMjx1U6PD4eCmRh0xGo0oLS1FNBpluNxOV1cXqqqq0NTUpHYpRAXjZpsaM4HCTY36ZbFYEAgENDc1pqlwkWUZZ8+exZ133slfdKJ5ymxqzNxYK51Oo6ysjJsaC0zm0u9oNKqpn6mmwmVwcBDhcJhTYkRzlEqlsrvkM5say8vLUV9fD4fDocmrimh+DAYDysrKGC630tXVBYfDgUWLFqldCpFu3GhTY2VlJRobG+FwODTd3JCUYbFY4Pf7kU6nNXNFn2bCJZ1Oo7u7Gw888IDapRBp3o02NVZVVaGlpQV2u52bGotMWVkZJElCNBrVzB17NRMuvb29iMfjnBIjuokbbWq02WxobW2F3W5nN4siJklSdmqM4XKdrq4uLFiwALW1tWqXQqQZN9vUWF9fD5vNppkpEFKfxWKBz+dDKpXSxBcN9SvAtTnjnp4e/OxnP1O7FCLV3WxTY1NTE6qqqjR1uSlpR2lpaXZqzGq1ql2ONsLl/PnzSCaTWLVqldqlEOXd1E2Nfr8fyWQSJSUlsNvt3NRIMyZJEiwWC8NlqjNnzqCxsRF2u13tUojyQpbl7KbGQCCQ3dRYXV3NTY00ZxaLBZFIJPsFRU2qh0ssFsOFCxfw5JNPql0KUU6l0+lpd2qUZZmbGklRZrMZBoMB0WiU4XLu3DnIsswpMSpIqVRq2p0ahRAoLy/HokWLuKmRFDd1aqyqqkrVWlQPl66uLixevFgzl88RzVcymZy2ByWzqbGpqYmbGinnLBYLwuEwEomEqvudVA2XcDiMgYEBbNq0Sc0yiOYtHo9nAyUUCkGSJFitVrS0tMDhcKg+RUHFw2w2w2g0IhqNFm+4nD17FpIkYcWKFWqWQTQn0Wg0GyiRSISbGkkzMgv7NptNtRpU/e3v6upCW1sb551JNyKRCHw+H/x+P2KxGAwGA+x2OxYtWsRNjaQZFosFoVAI8XhctWlY1cJlcnISw8PD2LJli1olEM1IKBTKBkrmxlp2ux3Nzc3c1EiaVFJSApPJhGg0Wnzh0tXVBZPJhGXLlqlVAtEN3WxTY+bGWlarlXtQSPMyC/tCCFV+X1ULlzNnzqCjo4PdW0kTbrSpsbS0FDU1NdlNjUR6YrFYEAwGEY/HszcUyydVwmV8fBxXrlzB2rVr1Xh7IgA33tRosViwYMECOBwOzd2TnGg2TCZTdmqsaMLlzJkzMJvNWLp0qRpvT0XsRpsaKyoq0NDQALvdzotLqKCUl5dn91rle2pMlXDp6urC8uXLeakm5cXNNjU2NzfDbrdzUyMVrLKyMkxOTiIWi+X9i1PeP91HR0cxPj6Op556Kt9vTUUmFAphaGho2qbGxYsXw263c1MjFQWTyQSz2YxoNKrPcDl27BgWLFgwo8dOTExg2bJlSCaTOHfu3Iyek0qlkEgksHr16vmUSQXg0qVLM14LicViSCQSqK2thdVqze5ByZy93OwS4lQqhbq6OsVqJlJaMBic8Rcko9GIZDKJWCw249cXQmT74M2VIuHi9XrxyCOPzPjx991334wfe/nyZXz++eewWq0MF0I0GsWiRYtm9FibzYaFCxf+5O8HBgYQiURgt9vR0NDwk3/v6+tjuJCmpVIpyLI8o+aUs532FUJgfHwcJpNJ/XABkJOdybIsY8+ePXjyySfR29ur+OuT/kiSNK9Ni729vYjFYmhqasLg4CBkWUZzczP3rZDuRCKRnNxILrM3Zr40u7VYCIHOzk5YrVbcc889apdDBSCZTMLn82H58uWw2+1YsWIFRkdHEY/H1S6NaNYMBgMikYjirxsKhRS5k6Vmw2V8fBynTp3Czp07+a2SFHHhwgXU1NRkr1IsLS1FQ0MDzp07p8g3NaJ8qqqqQjAYVPQ1M2stSuyL0WS4CCHwzjvv4IknnuDd+UgRQgiEQiEsWbJk2t83NDQgkUggmUyqUxjRHJWVlWXDQIs0Fy5CCHz11VcwmUx48MEH1S6HCkQgEIDBYPjJeo0kSairq0NPT49KlRHNTWZGR8lwCYfDMBqNiswWaS5cfD4fjh8/DqfTyekwUszAwAAWL158w39raWlBJBLR7DdAopsxmUwIhUKKvV4oFFLs9siaChdZluHxePDoo4+qepMbKixCCKRSKdTU1Nzw3w0GA0wmE8bGxvJcGdH82Gw2hMNhRV4rM8WmVMcKzYSLEAIfffQRKisrZ7Vnhuh2wuEwJEm65Zlwe3s7Ll68mMeqiOYvs5FSibPudDoNAIrNGGkiXIQQOHXqFM6fP48dO3ZwOowU1d/ff9uNl1arFUIIyLKcp6qI5i/zWZlIJOb9WoFAQNEWMaqHixACfX196OzsxI4dO9iVlm5rNt/ShBCIxWK3DRdJklBaWorLly/PtzyivLJarZiYmJjXawghkEwmFVtvAVQOFyEEuru7sXfvXjz33HM3bMVBdL2rV6/OOGBmc6rf3t6O0dHRedVGlG8VFRVIp9PzmhrLnLErOWukWrgkEgl8/fXXOHz4MJ577jmsXLmS02E0I0NDQzNexBwaGkJlZeWMfrfKy8uxYsWK+ZZHlFdKTI35/X5YLBZ9h4sQAgMDA/B4POjr64PT6cTy5csZLDRjLS0t6OnpmdE3Na/X+5ONkzcjSRLvPkm6VFVVhUAgMKfn5mJKDMjj/VyEEAgGg/j666/R19eH++67D2vWrIHZbM5XCVQg6urqMDg4iGQyecvfn0z4qHGLV6J8Ki8vx+Tk5JzuOBmPx+fdEPZG8nLmIoTAmTNn8N///d9IJpNwOp1Yu3Ytg4XmZKa76n0+n2K7jYm0TJIkmEymWfcaE0IgEAjAbrcrXlPOz1xkWcZXX32FH374AU8//TRWrlypeEJS8WlpacF3330HWZZv+vs0ODh40135RIXG4XBgbGwMVqt1xl+oUqmUohsnp8rpp7wsyzh06BDOnj0Ll8uFVatWMVhIEQaDARUVFRgcHLzhvwshkE6nUV1dnefKiNRhNBpn1YZfCAGfzzerMJqNnH3SCyFw6NAhDA0N4dVXX0VtbS2nJ0hRS5cuhdfrveHC/sTEBAwGA3/nqGhIkgSHw5Fde7mdRCIBWZZz1nk+J+EihMDhw4dx8eJFvPrqq6isrMzF21CRKykpgdlsvuHGx76+vhlfJUZUKEpKSmAymW4bMJmzFofDkbMvYIqHiyzL+OSTT9Df349XX32V92OhnJEkCcuWLcOlS5emtW1JpVKcEqOiJEkSqqurEYlEbnqPokywmM3mnKy1ZCgaLolEAgcOHMDg4CDPWCgvysrKUFFRgf7+/mxX197eXtjtdk6JUVEyGo2w2Wzw+XxIJpPTzmCEEJicnEQqlUJ1dXVOjxHFrhYbGhrCZ599BpPJhD/7sz/jGQvlRebs5YcffsDo6ChKSkoQDAaxevVqtUsjUo3FYkE6ncb4+DgqKythNpshyzLC4TBkWc7LGrhi4bJv3z7cfffdWLt2LUwmE2+8RDlz/e+W0WjE8uXLMTAwACEEli5dCoPBwN9BKmi3+/2urKxESUkJwuEwIpFItjlrph1Sro8PRcKlvLwca9asgcPhQF9fnxIv+RMLFy7MyeuSvphMppu2uaivr89Ojc21FQYAtoAhzTMYDIjH4zN6bHl5eTZIDAbDjHuQmUzziwdJKBBf+boHBvfIUL7ORrheQ1qmh+NAkXCZjXA4jAsXLmD58uXs+UQ5FQ6H4fV60dzczC8mVLQikQhSqZTijSlvJ+9HXCAQwNGjR/Ef//Ef6O7uzvfbUxEQQuDSpUs4c+YMotFo9p4uRMVElmX4fD4EAgFV1h/zfuYCALFYDIcOHUJ3dzdWr16Np556KnsvaKL5iMfj6OvrQzgcRkNDAxYtWsQpLio68Xg8Gyp2u12VWSJVwiXj1KlT6OzshM1mw7Zt27hoT/Pi8/kwMDAAo9GI9vZ27rOiopO5tUkoFEJpaSnsdjuMRqMqtagaLsC1mznt378fXq8X69atw5o1a9Qsh3RIlmUMDg7C6/WiuroaS5YsUe2AIlJLOp2G3+9HIpFAVVWV6l+uVA8X4Fq7ji+//BInTpzA0qVLsXnzZm7CpBmJRCLo7e1FIpHA4sWLUVtbq3ZJRHkXjUYRCARgMBjgcDg0ca8sTYRLxoULF/DRRx/BYDDgueeeQ2trq9olkYZduXIFw8PDsFgsaG9v59WHVHSEEJiYmEAkEoHFYtFU2yNNhQsAhEIhHDx4EP39/XjooYfw+OOPc4qDpkkmk+jv78fExATq6+vR1NSkmQOKKF+SyST8fj/S6TTsdjssFovaJU2juXABrqXxH/7wB3z55ZdYuHAhtm7dyg63BODafVr6+/sBAK2trbDZbCpXRJR/oVAIk5OTKCkpgcPhmPdu+lzQZLhkXL58Gfv370cwGMTGjRtx9913q10SqUQIgaGhIYyOjsJms6G1tZWXr1PRSafTCAQCiMfjqKyszNldJJWg6XABrrXx//TTT/HDDz9g1apVeOaZZ3J6DwLSnlgsht7eXkSjUTQ3N/OSdSpKsVgMgUAAkiTBbrdr/nNQ8+GScebMGRw+fBhlZWXYtm0bGhsb1S6J8mBsbAwXL16E2WxGe3s7m0pS0cncgyUcDqOsrAx2u10X7Yx0Ey7Atfn2ffv2YWRkBI8++ijWrl2r2VNCmp9UKoWBgQH4/X7U1dWhpaVFFwcUkZJSqRT8fn+2N5ietmjoKlyAaxvmjh07hm+++QbNzc3YsmVL3huyUW6FQiH09vYinU6jtbUVDodD7ZKI8i4cDmNychJGoxEOh0N3a4y6C5eMixcv4sCBA0gkEti8eTOWL1+udkk0T0IIjIyMYGRkBFarFW1tbZrYDEaUT7IsIxAIIBaLoaKiAlVVVbqcodFtuADXdqUePnwY3d3duPfee7F+/XrdpTtdk0gk0Nvbi1AohMbGRjacpKKUSCTg9/tVbTipFF2HS8bJkyfx6aefwm63Y9u2bViwYIHaJdEssOEkERAMBhEMBmE2m+FwOHS/ebwgwgW41gBz3759GB8fx5NPPokHHnhA7ZLoNmRZxsWLFzE2NsaGk1S0pjactFqtsFqtapekiIIJF+DalRVffPEFvv32W3R0dGDz5s28dFWj2HCSSJsNJ5VSUOGSwQaY2jY6OoqhoSE2nKSidX3DSZvNVnCX2hdkuADTG2A+/PDDeOyxxzjlojI2nCSa3nDSZrMV7OxKwYYL8NMGmNu2beOeCZWw4STRtS+9wWAQJpNJsw0nlVLQ4ZJx+fJl7Nu3D+FwGBs3bsRdd92ldklFQwiB4eFhXLlyhQ0nqWjpqeGkUooiXIBr1493dnbi9OnTuOOOO7Bp0ybNN37TOzacJPq/hpMA4HA4iuZzp2jCJaOrqwuffPIJLBYLtm7dygaYOeL1ejE4OMiGk1S09NpwUilFFy4AEAgEsH//foyMjOCxxx7DI488UvCnqPmSTqcxMDAAn8/HhpNUtPTccFIpRRkuwLUNfEePHsU333yDxYsXY8uWLQWzeUktUxtOLlmyhHcPpaIUiUQwMTGh24aTSinacMkYHBzEgQMHkEqlsHnzZixbtkztknRHCIHLly/j0qVLqKysRHt7e0FtBiOaiakNJ8vLy2Gz2Yp6RqTowwW4tkv20KFDOHfuHO677z6sX7++oC8RVFIikUBfXx+CwSAaGhrQ0NBQ1AcUFadCajipFIbLFN9//z0+++wzOBwObN26lQ0wb8Pv96O/vx9GoxFtbW2cVqSiVGgNJ5XCcLnO2NgY9u/fj/Hxcaxfvx7333+/2iVpztSGkw6HA0uWLOGZHhWdQm04qRSGyw2kUin89re/xR//+Ec2wLzO1IaTLS0tqKurU7skoryLRqOYmJiAJEkF13BSKQyXW+jp6cFHH30Eo9GILVu2YMmSJWqXpCo2nKRiVwwNJ5XCcLmNYDCIgwcPYmBgAI888ggee+yxovtlmtpwcuHChWhubuaiPRWdYmk4qRSGywwIIXD8+HF89dVXqK+vx9atW4umAWam4aQQAm1tbWw4SUWpmBpOKoXhMgsjIyPYv39/UTTAZMNJomsXr/j9/qJqOKkUhsssJRIJHDlyBP/7v/+LO++8Exs3biy4RnRTG042NTWhvr5e7ZKI8i4ej8Pv9wMoroaTSmG4zFFXVxcOHz6M8vLygmqAyYaTVOyKveGkUhgu8xAIBLBv3z5cuXIFjz32GB5++GHdnjJPbThZW1uLxYsX84CiosOGk8phuMyTLMv4+uuv8bvf/U63DTDZcJKIDSeVxnBRyMDAAA4ePKirBpiZhpMjIyOoqKhAW1sb55Wp6MiyjImJCUSjUTacVBDDRUHRaBQff/wxzp8/r/kGmGw4STS94aTNZoPFYlG7pILBcMmB7777Dp9//jkcDge2bdumuRYpfr8fAwMDMBgMbDhJRYsNJ3OL4ZIjY2Nj2LdvH/x+P9avX4/77rtP7ZLYcJIIbDiZLwyXHJraAHPZsmXYvHmzaqfdkUgEfX19iMfjbDhJRYsNJ/OH4ZIH58+fx8cffwyTyYQtW7Zg8eLFeX3/qQ0n29raOK9MRYcNJ/OP4ZInwWAQBw4cwODgYN4aYKZSKfT39yMQCGDhwoVoamriAUVFhw0n1cFwySMhBH7/+9/j66+/xqJFi7B161bY7facvNfk5CT6+voghEBra2vO3odIy9hwUj0MFxWMjIxg3759iEQi2LRpE+68807FXntqw8mqqiq0tbVxMxgVHTacVB/DRSXxeBxHjhzBjz/+iLvuugsbN2686eKiEALj4+MIhUKorKxETU3NDQ+UWCyGvr4+RCIRNpykgjPT44ANJ7WBE/AqKS0txZYtW7BlyxacO3cOv/71rzEyMjLtMYFAALt27UJHRwfq6urQ2tqKuro6dHR0YNeuXQgEAtnHer1edHV1IZ1OY+XKlQwWKhgzPQ4yDSfHx8dRUlKCBQsWMFhUxDMXDfD7/di/fz+uXLmCxx9/HA899BA+/fRTbN++HZFIBMC1Aycj822tvLwc77//PpYvX86Gk1SQOjs7Z3wcPPDAA0ilUrBaraisrFSlXvo/DBeNmNoAc3JyEv/6r/+a/fubkSQJkiRh165d2LFjBxtOUkHp7OzEs88+CyHEjI6Dd999F88//zzXGDWC4aIxp0+fxgMPPIBkMomZ/GgkSYLFYsGlS5d4RRgVjEAggKamJkSj0VsGSwaPA+3h/InGfPnll0gkEjMKFuDaNEE0GsXbb7+d48qI8uett95CJBKZUbAAPA60iGcuGiKEQEdHR3Z/ykxJkoS2tjb09PTwckvSPR4HhYHhoiFer3dePb+8Xi9qamoUrIgo/3gcFAZOi2lIKBSa1/ODwaBClRCph8dBYWC4aMh8L59k63AqBDwOCgPDRUNqamrQ3t4+6/liSZLQ3t7OS5GpIPA4KAwMFw2RJAmvvfbanJ77+uuvcxGTCgKPg8LABX2Nme31/QaDARaLBcPDw7y+nwoGjwP945mLxtjtduzduxeSJN22jYvBYIAkSfjwww95QFFB4XGgfwwXDdqwYQMOHToEi8WSbW0xVebvLBYLDh8+jKefflqlSolyh8eBvjFcNGrDhg0YHh7Gm2++iba2tmn/1tbWhjfffBOXLl3iAUUFjceBfnHNRQeEEPD5fAgGg7BaraiuruaiJRUdHgf6wnAhIiLFcVqMiIgUx3AhIiLFMVyIiEhxDBciIlIcw4WIiBTHcCEiIsUxXIiISHEMFyIiUhzDhYiIFMdwISIixTFciIhIcQwXIiJSHMOFiIgUx3AhIiLF/T+syUDAe4xTigAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=3, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.01, lamb_entropy=2.);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b17e4ed5",
   "metadata": {},
   "source": [
    "$G=5$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1209c59c",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 7.47e-02 | test loss: 6.52e-02 | reg: 6.12e+00 : 100%|██| 20/20 [00:12<00:00,  1.58it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lpUW8+eabIicnRwAIfuXk5Ig333xTtLS0KF2i6nDM2ofjFj6OWfvobdw0Fy7r168XSUlJQpIkIUnSab+EwPeSkpLE+vXrlS5VNThm7cNxCx/HrH30OG6aCpf169eLmJgYYTAYThv8M78MBoOIiYnR1C8iUjhm7cNxCx/HrH30Om6SENqY0DObzejduzecTif8fv9FH28wGGA0GlFXVweTyRT5AlWIY9Y+HLfwcczaR8/jppkF/bKyMjgcjpB+AQDg9/vhcDjw4YcfRrgy9eKYtQ/HLXwcs/bR87hp4shFCIHc3FzU1NSEdeaEJEnIzs7GgQMHIElSBCtUH45Z+3Dcwscxax+9j5smwqWpqQlZWVkden5mZqaMFakfx6x9OG7h45i1j97HTRPTYjabrUPPt1qtMlWiHRyz9uG4hY9j1j56HzdNhEtycnKHnp+SkiJTJdrBMWsfjlv4OGbto/dx00S4ZGZmIicnJ+z5RUmSkJOTg4yMjAhVpl4cs/bJzMxEdnZ2u54bjeN26NAhvPPOO4iPjw/7ufys6Xsb1US4SJKEkpKSdj33qaeeUvWiV6RwzMLn9/thtVoxefLkdj3/iSeeiIpx8/l82LhxIx599FGMGDECH330EfLy8tr1WtH6WQP0v41qYkEf0Pf54JHCMQuNEAJOpxN2ux2SJMHj8SA3NzfkcZMkCUajEV988QW6deuGjIyMdu3Jq11DQwOWLFmCqqoq1NfX48Ybb0RRURHuueceOJ3OsD5rgTE7duxYVH3WzqTnbVQTRy4AYDKZUF1dDUmSYDBcuGyDwQBJkrB8+XLV/wIiiWN2cS6XC83NzbDZbOjSpQsyMjLQs2fPsMbNYDBgxYoVyM3Nhc/nw/Hjx3HixAn4fL5O+ikiRwiBL7/8EiUlJbj99ttRWlqKYcOGYfXq1Vi6dCnuu+8+JCQkhPVZC+xxT5gwoTN+BFXT9TbauQ0BOi7UHjwbNmxQulTV4JidzePxiJaWFlFfXy9aWlqEx+M56zHtGTe/3y8sFos4cuSIOHLkiLBYLMLv93fmjyaL1tZWUVZWJkaOHClycnLEyJEjRVlZmWhtbb3g80Ids6VLl4qXXnpJvPzyy6KpqamTfir10uM2qrlwEeJk99C33nrrnN1D33rrLWE2m5UuUXU4Zif5fD7R2toq6uvrRVNTk2hra7vg49s7bl6vVzQ1NYlDhw6Juro64XA4IvHjyG7v3r3ihRdeENdcc43o37+/mDFjhtixY0dYARnqmDU3N4uZM2eKP/7xj6KhoSFSP5Jm6G0b1cyay7mIf94vwmq1IiUlBRkZGapf5FJaNI9ZYF1FCIGkpCQYjcaQf/b2jpvb7UZzczPa2tqQmJiI9PR0xMXFdfRHkZXL5cL69etRXl6O3bt3o3v37pg0aRImTJiAbt26tft1Qxmz1tZWzJ07F3a7HdOmTUPPnj07+uNonl62UU2HC1Eo3G43bDYbvF4vunTpguTk5IvOb8vNbrejpaUFPp8PqampSEtL6/QaznT06FFUVVVhyZIlMJvNGDp0KAoKCnD33XcjJiam0+qw2WyYO3cuLBYLpk2bhl69enXae1PkMFxIt3w+H2w2G1wuF+Li4pCSkoLY2FjF6hFCwGKxwGKxwGAwID09vcMX0oXL5/Nh8+bNqKysxObNm5GSkoL8/HwUFBTg8ssv79RaTuVwOFBaWorGxkYUFxejb9++itVC8mC4kO4IIeBwOOBwOCBJEpKTk9GlSxelywryer1oaWmB3W5HfHw8MjIyIl7fiRMnsHTpUlRVVeHYsWO49tprUVhYiNGjR8NoNEb0vUPV1taGd999F8eOHcNvfvMb5OTkKF0SdQDDhXSlra0NNpsNQggkJiYiMTFRtfPVgdOgXS4XkpKSkJ6eLuuRlRACu3btQkVFBdatW4eYmBiMGTMGBQUFuO6662R7Hzm53W689957OHz4MKZOnYr+/fsrXRK1E8OFdMHj8cBms8Hj8SAhIQHJycmdum7QETabDS0tLfD7/UhLS0NaWlqHAtFut2PlypWoqKjAvn370LdvXxQWFuLXv/61Jq6P8Hg8WLBgAQ4cOIDJkydjwIABSpdE7cBwIU3z+/2w2Wxoa2tDbGwsUlJSVHc2Vij8fj8sFgtaW1sRExOD9PR0JCUlhfUaBw4cQEVFBVasWAGn04m7774bhYWFGDx4sOInD4TL6/Xiww8/xN69e/HQQw/h+uuvV7okChPDhTTpzHWVwKnFWufxeNDS0gKHwxHsGHChVjIejwcbN25EeXk5vvrqK2RlZWHixImYOHGi5k/r9fl8qKysxDfffIOCggIMHDhQ6ZIoDAwX0hyXywWbzQafz4fExEQkJSWpdl2lvZxOJ5qbm+HxeJCSkgKTyXTaNN/x48exaNEiLFmyBE1NTbjllltQWFiIESNGaPLI7Xz8fj8WL16Mr776ChMmTMCtt96qdEkUIoYLaYbX64XNZoPb7UZ8fDxSUlI0s67SHkIIWK1WmM1mAEBqaiq+++47VFRU4LPPPkNiYiIeeOABFBYWol+/fsoWG0FCCFRXV2Pbtm3Iz8/H0KFDlS6JQqDcSf9EIfL7/bDb7XA6nYiJiYHJZNJl1+EzSZKE1NRUeL1eLFy4EIsWLcIvv/yCAQMG4E9/+hPGjh2LxMREpcuMOEmSkJ+fj7i4OFRXV8Pj8WDYsGFKl0UXwXAhVXM6ncHbwSYnJ4fVskXLhBDBo5Q1a9ZACIG8vDyMHj0a/fr1Q2Jioq6mvy5GkiSMHTsW8fHxWLVqFdxuN0aOHBkVnwWtYriQKp3assVoNCIpKUlzZzy1h9PpxJo1a1BeXo49e/agd+/e+Ld/+zeMHz8+eOdBh8OB5uZmHD9+PLgeEw1jI0kSRo0ahbi4OKxduxYejwejR49mwKgU11xIVdTWsqWz1NTUoLKyEsuXL4fVasVdd92FwsJC3H777edcVxJCoLW1FWazGQaDASaTSfX3VJfT5s2b8dFHH+GOO+7A/fffz4BRIYYLqYIQAna7HQ6HAzExMUhOTkZCQoLSZUWUz+fDpk2bUFFRge3btyM9PR0TJ07Egw8+iN69e4f8Gi0tLbDZbJ3WSkYttm/fjqVLl+K2227D+PHjGTAqw3AhxWmpZYscGhoasGjRIixatAgNDQ246aabUFhYiFGjRrX7RIVIt5JRq6+++gpVVVUYNGgQHnzwwaiYHtQKhgspxuPxwGq1BlvhJyUl6fbUYiEEduzYgYqKCnzyySeIj4/H/fffj4KCAlx11VWyvY/dbkdzc7NsrWS0YPfu3SgvL8d1112HoqIi3X6GtIbhQp3O5/PBbrdrvmVLKFpbW7FixQpUVlbi4MGD6NevH4qKinDfffdFbI3k1FYyBoMBGRkZYbeS0Zrvv/8eZWVluOqqq/DII49ExVGb2jFcqNOovRW+nPbs2YOKigqsXr0abrcbeXl5KCoqws0339xpRxJerxfNzc1wOBxISEhARkaGrtexfvrpJ8yfPx85OTmYMmVKVFwLpWYMF+oU0dCyxeVyYd26dSgvL8e3336LHj16BG8XnJWVpVhdbW1taG5uhtvtRnJyMtLT03U7dXTgwAG899576NOnD6ZOnarrMFU7hgtFlNfrhdVq1WQr/FDV1taisrISy5YtC94uuKioCMOGDVPNzyqECLb2B4C0tDSkpqbqLuAB4NChQygtLUXPnj1RXFys26NjtWO4UESc2rIlNjYWycnJupqmCNwuuLy8HJ9//jnS0tIwbtw4TJo0CZdddpnS5Z2X3++H2WyG1WpFTEwMMjIydNlCpra2FqWlpcjMzERxcbHu15zUiOFCshJCwOl0wm63A/j/li160dTUFLxd8PHjx3HdddcFbxespT1kj8eD5uZmOJ3OkFr7a9Hx48cxd+5cpKSkYNq0aVF1kakaMFxINm63G1arFT6fT1ctW4QQ2LlzJyoqKrB+/XrExMRg7NixKCgowLXXXqt0eR1yamv/1NRU3bWSqa+vx5w5c9ClSxdMnz4daWlpSpcUNRgu1GE+nw9WqzXYCj85OVkXp4LabLbg7YL379+Pyy67LHi7YD39kTqztX96ejqSk5N1sx7T1NSEOXPmwGAw4Mknn0R6errSJUUFhgu1m15btuzbtw+VlZVYsWIFXC4Xhg8fjoKCAtx222262qs/06mtZOLi4pCRkaGbKc2Wlhb87W9/g8/nw5NPPomuXbsqXZLuMVyoXQLrKkKI4C2Gtbyn63a7sWHDBlRUVGDnzp3IysrCgw8+iIkTJ6JHjx5Kl9ep3G43mpub0dbWhsTERGRkZOjiSNRisWDOnDloa2vDtGnTou732tkYLhSWM1u2JCcna3pv/tixY8HbBZ84cQK33norioqKMHz4cF38Qe0Iu92OlpYW+Hw+pKamIi0tTdO/a+DkVOecOXNgtVoxbdo0XHLJJUqXpFsMFwrJma3wk5OTNduyxe/3Y+vWrSgvL8ff//53JCYmIj8/HwUFBcjJyVG6PFURQsBiscBiscBgMATXY7TMbrejtLQUJ06cQHFxMfr06aN0SbrEcKEL0lPLlpaWFixbtgyVlZU4evQorrrqKhQVFWHs2LG6WVuIFK/Xi5aWFtjtdl20kmlra8O8efNw/PhxPP7448jOzla6JN1huNB56aEVvhAC3377LSoqKrB27VoIITB69GgUFRXh+uuv19zPozQ9tZJxuVx47733UFtbi6lTpyI3N1fpknSF4UJn0UPLFqfTidWrV6O8vBx79+5F7969UVhYiHHjxvFUVBkEWslovbW/x+PB+++/j59//hlTpkyR9fYH0Y7hQkF+vx82my3YCl+LLVsOHjwYvF2wzWbDsGHDgrcL1vpitNqc2to/JiYG6enpmmyz4vV6UVZWhh9//BGPPPKI5i+MVQuGC53WskWSpOCpxVrh9XqDtwv+4osvkJGRgQkTJoR1u2BqP4/Hg5aWFjgcDs22kvH5fCgvL8d3332HoqIi3HjjjUqXpHkMlyh3ait8rbVsqa+vx+LFi4O3Cx40aBAKCwuRl5enuT9uenBqK5mUlBSYTCZNTaf6/X4sWrQIO3fuxIMPPoh/+Zd/UbokTWO4RCmv1wubzaa5li1CCHzxxReoqKjApk2bkJCQgAceeAAFBQW44oorlC4v6p3ZSsZkMiElJUUz6zFCCCxbtgzbt2/HuHHjMGTIEKVL0iyGS5Q5tRW+llq2WCwWLF++HFVVVaipqUFubm7wdsFav+5Cj3w+X7C1v9ZayQgh8NFHH+Hzzz/H/fffjzvvvFPpkjSJ4RJFtNiy5YcffgjeLtjr9eKee+5BYWEhBg0apPra6fRWMkajERkZGZq4+FYIgXXr1mHTpk341a9+hREjRihdkuYwXKKA2+2GzWbTTMuWtrY2rFu3DhUVFfj222/Rs2dPFBQUYPz48Ww4qFEOhwPNzc3w+XzB9Rg1fwYDNm7ciI8//hgjRozAqFGjuEMTBvVPslO7ndmyRe0NCI8cOYLKykpUV1fDbDbjjjvuQGlpKe666y5NLQzT2RITE2E0GtHa2gqz2Qy73R5cj1GzkSNHIi4uDqtWrYLH48HYsWMZMCFS718aardAK3yn0wlJkpCamqrali0+nw+fffYZKioqsGXLFphMpuDtgvv27at0eSQjSZKQlpaG5ORktLS04MSJE7BarcjIyFDt5xMAhg0bhri4OFRXV8Pj8SA/P58BEwJOi+mMVlq2NDY2Bm8X/Msvv+D6669HUVERRo0apeo/NCQfl8uF5uZmuFwuJCUlIT09XdVH1l9++SUWL16Mm2++GRMnTtTEtJ6SGC464fF4YLPZ4PF40KVLFyQlJaluKilwu+Dy8nKsX78ecXFxGDt2LAoLC3H11VcrXR4pREutZHbt2oWKigpcf/31KCwsVN02piYMF407s2VLSkqK6s7Gsdls+Oijj1BRUYEDBw4gOzsbBQUF+PWvf43U1FSlyyMV0FIrmW+//RYLFy7EgAED8PDDD6v6aEtJDBeNOrMVvhpbtvz000/B2wW73W6MGDEChYWFuPXWW1W7Z0rK8nq9aG5uhsPhQEJCAjIzM1XZbWHv3r1YsGABcnNzMXnyZNXt0KkBw0WDTm3ZkpiYiKSkJNX8sXa73Vi/fj0qKirw9ddfo1u3bsHbBXfv3l3p8kgjTm0lo9bW/vv378f8+fPRt29fTJ06VZUhqCSGi4ac2bIlJSVFNRtcXV1d8HbBzc3NGDx4MAoKCni7YGo3IURwPQYA0tLSkJqaqpodKQCoqanBvHnzcMkll+Dxxx/nySinYLhohNVqDbZsSUlJUc1eUmNjI1544QV89tlnSE5ORn5+PiZNmsTbBZNs/H4/zGYzWltbERcXh65du6qqZdGRI0dQWlqKrKwsFBcXIzExUemSVIHhoiC73R7yXr3NZoPBYDjnBzfwKzzXHp3f72/XWszs2bPRv3//iz5OCIGGhgYkJSWdc3qura0NCQkJ56ytpaUFEydODLs20hez2Yy4uLiLHpG43W5YLBaYTKaw1jiEEPD7/WFfsLlhwwb07NkzpMfabDYcOnQIAwYMCHk2wev1wuVy4bbbbgurLq3gfIWCvF5vyHs5GRkZ5/2/1tZW+P1+mEymc/5fe8LlwIEDKC4uDvt5pwpcx5Kbm4tXX331rI3u6aefZrgQPB4P2traLromZzQakZaWFtZr+/1+NDQ0BM+kDEd9fT1uvvnmkN/zlltuCfm1rVYrFixYgPT0dN2GC68CUpgkSR36crvdcLlcwb2gM/+/I3XFxcW1+2vnzp2YOXMmpk+fjv379+PFF1886zFEAS6XC263u8Pbw5lfNpsNfr+/3XW9/fbb8Hg8iImJkfWrqqoKmZmZMo6g+jBcNK61tRWpqalITU2F1WpVuhwAJ6chiouL8frrr2PUqFFYuHAhli9fDrvdrnRppFIpKSk4ceKE7K/b2tp6ziP6UF166aUoKyuTryCc3D4OHDiA8ePHy/q6asNw0TAhBIQQSEhIQHx8fPDfSquurkZCQgJGjRoFAEhPT8fgwYPx7LPPKlwZqZXJZILH45H9df1+f4cW2IuKirBv3z5Zt6vATpbezyxjuGjYmdNgaiCEwIsvvoi5c+eeVtPbb7+NjRs3qiL8SH0CnxU5Px9yvFZCQgLi4uLw888/y1DRSdXV1bjiiitUs81GCsNFw2w222l3YTQYDGhra1OwIuD48ePwer0YOHDgad9PTU1FYmIitm3bplBlpGaBP7QdWR85U+C1OvpHfPTo0aisrJSjJADAd999hwkTJsj2emrFcNGowOmVpx5aG41Gxdc1SkpKMHHixLM2aEmS8OKLL+Lf//3fFaqM1C42NlbWdcPAdTEdNWTIEFgsFlmOhPx+P4QQHVoH0gqGi8ad+kfcaDTKuucXLiEEvv/+ezz//PPn/P/7778fLS0tcLvdnVwZaUFaWpqs4WKz2WRpjBo4hd5isXT4tb777jtN3F5cDgwXjXI4HGddNxKJeetw7N27F3Fxcee9rsZgMCA7OxuzZ8/u5MpICxITE2WfFpPravkBAwZg+fLlHX6dFStWYMyYMTJUpH4MF42y2+1nXRSm9N7Q008/jSeeeOKCj5kzZw7mzZvHhX06i5w7RxfqWtEe+fn52LNnT4deQwgBq9WKm2++WZaa1I7hojC32x32xhR4/Pnmk30+X4frCpcQAocOHbpouGRnZyMmJgb/+7//20mVkVbIuXMkd7iYTKbgOmd72Ww2AFBNs9lIY7gozGKxhH1+/4XOgomNjYXT6ZSltnAcPHgQsbGxF22oKUkSXnvtNV7zQuclx5qc0+mU9TbEkiQhISEBP/30U7tf46OPPkJubq5sNakdw0VhKSkpMJvNYR29WK3W83aFTUxMlO105EOHDoX82KeffhoPPfRQSI8dM2YM3nvvvfaWRTpmNBplWTi3WCynnaYvh3vuuQfLli1r9/O/+eabqDgFOYDhorCEhAQYDIaQjzaEEHC73edtwhe4Ul8O48ePD6klhxACP/30E55++umQXleSpKjag6PQpaamynLk7fF4wm5UeTFDhgwJe0cwwOv1QghxwQa0esNwUZgkSUhLS4PNZgvpQ3uxC8PkXBTNy8vDY489dtHHHT16FDExMbpvZ0GRJ8d9WgKffbnXNgKv19raGvZzN2/ejIyMDMVPuulMDBcVCNzTxev1XvSxFosFXbp0uWi4yOHFF1/Enj17gguR5/P0009jwoQJUbXhUGSdb+fI7/fD6XTC5XJddAdK7s+jJEm44YYbUFVVFdbzhBDYsGEDioqKZK1H7RguKiBJEpKSki461yyEgNfrDelwX44zxuLj43HnnXfimWeeuWBN3333HX7/+993+P2ILtQGxu/3o76+Hi0tLWhsbERLS8s5A8bhcMi6mH+qcePGYf/+/WHNDDidTni9XvTt2zciNakVw0UlAheQXehDa7VaERsbe9E9stjYWDgcDlnq+utf/4pPP/30vKdgfvPNN4iPj+etXUk2sbGxZx0tB+54ajAY0KNHD3Tv3h02m+2cV/SbzWZZrsw/F6PRiNjY2LAaWS5cuBDXXHNN1B3ZM1xUQpKkC/ZW8vl8aGtrC6knUVJSElwulyx1paSkoGvXrli0aNE5/7+kpISnFZOs0tLSzlrX8Hg8cLlc6NatGwwGA+Li4tCjRw+0tLScteMT6tF9e0iShPHjx6OsrCykoxe32419+/ahoKAgIvWoGcNFRUwmE9ra2s760Aoh0NLSgsTExJAO9+U8Yww4eVX9zJkzz3pNm82G+vr6qJtLpshKSko6LTACRy0mk+m0vf9Aq6HGxsbgZ1PuiyfPZdCgQXC73Re95kUIgYULF6J///5RebILw0VFTj16OXVjsVgsMBgMSEpKCuv15AqYG264AQaDATt27DjttUtKSnD33XdHzRXH1LkCn1+fzwefz3fWVJckSejatSva2tqCJ8NYLJaQpo47QpIkPPzww/jggw8uOP184MAB/Pjjj5g8eXLEalEzhouKSJIEk8kEl8sFu90Ol8sVPOw/c6/tYq8DyHdvDEmS8Oc//xnTp08Pnihw8OBBbNu2DX/5y19keQ+iAEmSEBMTg9bWVgghUF9fj9TU1HN+/g0GA0wmE+rr6+H1emGxWJCVlRXxGq+++mpcc801mD179lknFgghUFNTg/nz56OoqEiW06u1iOGiMoGNxePxwG63Iz4+Hunp6WGf/RIfHy9r+/Jf/epX6Nq1K/7rv/4LX3/9NQoKCvDMM89wIZ8iIisrC2azGXa7HT6f74JrjampqYiPj0d9fT26dOkiyz1cLkaSJBQUFKBXr154++238dlnn+HIkSOoqanBmjVrMH/+fIwePRrXX399xGtRq1ilC4h255q6io2NPWtjCneKK9BWJnANjRy1VVVVoaSkBM8//zwmTJiAqVOnsrsxyeLMz1F8fHywFUy3bt3O+ZhTZWVlwe12B3vbyfW5vNDrGAwGTJo0Cd9//z127NiBL7/8EpIkoXv37pg6dSouu+wyWWvRGoaLggwGQ0RvnNWR+2Okp6fjk08+Oev7hYWFsNvtSE9Px6ZNmzpU31VXXdWh55M+xMTEnLPlS2BhP3DhZCjO97j2HM0kJSXh+++/v+jjJEnCLbfcAqfTCUmSYDQaYbVaQ3pur169wq5LKyQRrbGqAp019O1Z3AylW0BHBebWKbqpdTvojFtXSJIUsQs+lcZw0QghBHw+H2JiYlR1MZbf70djYyNMJlPULlxS5xFCwOPxIC4uTlXbgd1ux8GDB3HllVde9LYT0UKfkalDPp8Pzc3NitwI7EJeeeUV/Ou//ivq6uqULoWigMfjwfHjx8O+B1Ik+Xw+vPPOO1i3bp2qAk9pDBdqt61bt6KsrAzPPvsscnJylC6HSBEbN27E8ePHUVhY2ClnqmkFw4XaxWKx4LnnnsPgwYNDvkkYkd4cOXIEn3zyCfLy8nDppZcqXY6qMFyoXV566SU4HA78+c9/1u2CJNGFuN1ulJeXo0+fPhg+fLjS5agOT0WmsK1btw6rVq3CG2+8gZ49eypdDpEiVq1aBYvFgscff5w7WOfAEaGwNDQ04A9/+ANGjRqFsWPHKl0OkSJ++uknbNu2Dffdd1+ntJvRIoYLhUwIgeeeew4JCQl4+eWXeWYMRSW73Y6qqipceeWVGDx4sNLlqBanxShklZWV2LJlC95///2Q7itDpDdCCCxbtgxerxcPPvggd7AugEcuFJJDhw7htddeQ2FhIe644w6lyyFSxK5du/DNN99g/PjxSEtLU7ocVWO40EX5fD4888wz6NGjB37/+98rXQ6RIsxmM5YtW4abbroJN9xwg9LlqB6nxeii5s6di++//x5LliyB0WhUuhyiTieEQFVVFRISEpCfn690OZrAIxe6oB9++AGzZs3CtGnTuLdGUWvLli3Yv38/CgoKeA+jEDFc6Lza2trw29/+FldeeSVKSkqULodIEfX19Vi9ejVuv/129O/fX+lyNIPTYnRer7/+Ourq6rBy5coO3XSMSKt8Ph8qKiqQkZGBe++9V+lyNIVHLnRO27dvxwcffIDf/e536Nevn9LlECnik08+wbFjx1BUVMRW+mFiuNBZWltb8eyzz2Lw4MF4+OGHlS6HSBGBppQjR45kU8p2YLjQWV566SXY7XY2paSo5Xa7UVFRgd69e2PEiBFKl6NJnEin03z88cdYuXIlm1JSVFu1ahXMZjN+85vfcAernThqFBRoSnnPPfewKSVFrUBTyrFjx7IpZQcwXAjAyYvEnn/+ecTFxWHmzJnsmURRyeFwoKqqCldccQWGDBmidDmaxmkxAgBUVVVh8+bNmD9/PptSUtQKNKWcNGkSd7A6iEcuhMOHD+O1115DQUEB7rzzTqXLIVLErl27sHv3bowbN45NKWXAcIlyPp8Pv/3tb9GtWzc8//zzSpdDpIhTm1LeeOONSpejC5wWi3LvvPMOm1JSVAs0pYyPj2dTShnxyCWK/fDDD3j77bfxxBNPsCklRa2tW7di//79mDRpEptSyojhEqUCTSmvuOIKNqWkqNXQ0IBVq1bh9ttvxxVXXKF0ObrCabEo9cYbb+Do0aNYtWoV4uLilC6HqNP5fD6Ul5ezKWWE8MglCn3xxRdYsGABm1JSVAs0pSwsLGRTyghguESZQFPK2267DY888ojS5RApora2NtiUsk+fPkqXo0sMlyjz0ksvwWq1siklRS23243y8nL07t0bw4cPV7oc3eKaSxRZv349Vq5ciddffx2XXHKJ0uUQKWL16tUwm82YOnUqYmJilC5Ht7jrGiUaGhrwn//5n7jnnntw3333KV0OkSL27duHrVu3YsyYMejWrZvS5egawyUKBJpSxsbG4uWXX2bPJIpKpzalHDp0qNLl6B6nxaLAokWLsHnzZrz77rtIT09XuhwiRSxbtgxut5tNKTsJj1x07siRI3j11VcxadIkDBs2TOlyiBSxe/du7N69G+PHj2dTyk7CcNExn8+HZ555BllZWWxKSVHLYrFg6dKluPHGG9mUshNxWkzHSktL8e2332Lx4sXsmURR6dSmlOPGjVO6nKjCIxed2rNnD9566y0UFxdzb42i1tatW7Fv3z42pVQAw0WHXC5XsCnlU089pXQ5RIpoaGjA6tWrMXToUDalVACnxXTo9ddfR21tLVauXMmmlBSVfD4fKioqYDKZMGbMGKXLiUo8ctGZHTt2YMGCBXjmmWeQm5urdDlEiti0aRPq6upQVFTEppQKYbjoiNVqxe9+9zvceuutePTRR5Uuh0gRtbW12LhxI0aMGMGmlApiuOjIn/70J1itVvzP//wPm1JSVHK73aioqECvXr0wYsQIpcuJavwLpBPr16/HihUr8OKLL7IpJUWtNWvWoLm5GUVFRWxKqTCGiw4EmlLm5eXh/vvvV7ocIkXs27cPW7ZswdixY9mUUgUYLhonhMB//Md/IDY2FjNnzmTPJIpKgaaU/fv3Z1NKleCpyBq3ePFi/P3vf2dTSopq1dXVbEqpMjxy0bDa2lq88sormDhxIptSUtTavXs3du3ahXHjxsFkMildDv0Tw0UDhBBoampCbW0tmpqaIIQINqXs2rUrXnjhBaVLJIq4wHZQV1cX3A4sFguWLVvGppQqxGkxFTObzSgrK8OsWbNw8ODB4PdzcnJw0003YdeuXViyZAl7JpGunW87yM7OxsCBA5GdnY1x48ZxOkxlGC4qtWHDBuTn58PhcJz1fwcPHsTBgwcRHx+PxsZGBaoj6hwX2g5qampQU1MDo9GIYcOGIS8vT4EK6XwkIYRQugg63YYNGzB69GgIIeD3+8/7OEmSYDAYsHbtWm5YpDuhbgcGgwGSJHE7UBmGi8qYzWb07t0bTqfzghtUgMFggNFoRF1dHRczSTe4HWgfF/RVpqysDA6HI6QNCgD8fj8cDgc+/PDDCFdG1Hm4HWgfj1xURAiB3Nxc1NTUIJxfiyRJyM7OxoEDB7ioSZrH7UAfGC4q0tTUhKysrA49PzMzU8aKiDoftwN94LSYithstg4932q1ylQJkXK4HegDw0VFkpOTO/T8lJQUmSohUg63A31guKhIZmYmcnJywp4vliQJOTk5yMjIiFBlRJ2H24E+MFxURJIklJSUtOu5Tz31FBcxSRe4HegDF/RVhuf3E3E70AMeuaiMyWRCdXV18Or7Cwlcmbx8+XJuUKQr3A60j+GiQnl5eVi7di2MRiMkSTrrMD/wPaPRiHXr1mHkyJEKVUoUOdwOtI3holJ5eXmoq6vDm2++iezs7NP+Lzs7G2+++SaOHTvGDYp0jduBdnHNRQOEEGhubobVakVKSgoyMjK4aElRh9uBtjBciIhIdpwWIyIi2TFciIhIdgwXIiKSHcOFiIhkx3AhIiLZMVyIiEh2DBciIpIdw4WIiGTHcCEiItkxXIiISHYMFyIikh3DhYiIZMdwISIi2TFciIhIdv8Hx6GppnpAU7oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.01, lamb_entropy=2.);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0de00173",
   "metadata": {},
   "source": [
    "$G=10$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9d67a57a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 8.08e-02 | test loss: 7.24e-02 | reg: 5.89e+00 : 100%|██| 20/20 [00:13<00:00,  1.44it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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mHDx4EJ9//rmq7mOKFRfvkUddaYv6RijkgEz4i/d1EspIOZBjEERdMMaQl5eHr776CgsXLkRcXJzcIQWEKsQFqN2RfT05ehtT0tMj4S/+mpn6eg1dZ4QYOBwOrFq1Cjt27MC7776Ldu3ayR1SwChWXDzhO3V9Ixjv1/pKjRGEL4K9RjyvS1//JohAYYzh559/xqeffgqbzYYPPvgA99xzj9xhBYUqxAWoO21R12iGhyZeCSmh640IFovFgk2bNuE///kPhgwZgqefflqxppT+oBpxARrusNShCamh0QoRCowx2O12HDlyBKtWrUJcXBxmz56Njh07qv5+pipx8aautAT//94lpgQhJrTGimiIsrIy6HQ6OJ1OlJWV4dSpU9i7dy/sdjtGjRqFrKwsREZGyh2mIKhaXID6OzHNuxBSUN9DDkF4Mnv2bGi1WnAch4iICLRt2xZPPvkkevbsCb1eH1bXjmLFJZgRR30T/DSCIepCqGuDFu4S9aHT6fDEE0/A4XAgMjIS8fHxbkE5ffq0IOdo3ry5IMcRAg1TYC+QKqRwekoggoOuNUIqbDab6OfQarWKSaspUlwChVJfBEGEEy6XC1arFTExMYreEKw+VG+5zxgDx3GUhiAkgeM4uUNQHdQ3A+fq1at47rnncPXqVblDCRrViwtBEAShPEhcCIIgCMEhcSEIgiAEh8SFIAiCEBwSF4IgCEJwSFwIgiAIwSFxIQiCIASHxIUgCIIQHBIXgiAIQnBIXAiCIAjBIXEhCIIgBIfEhSAIghAcEheCIAhCcEhcCIIgCMEhcSEIgiAEh8SFIAiCEBwSF4IgCEJwSFwIgiAIwSFxIQiCIASHxIUgCIIQHBIXgiAIQnBIXAiCIAjBIXEhCIIgBIfEhSAIghAcEheCIAhCcEhcCIIgCMEhcSEIgiAEh8SFIAiCEBwSF4IgCEJwSFwIgiAIwSFxIQiCIASHxIUgCIIQHBIXgiAIQnBIXAiCIAjBIXEhCIIgBIfEhSAIghAcEheCIAhCcEhcCIIgCMEhcSEIgiAEh8SFIAiCEBwSF4IgCEJwSFwIgiAIwSFxIQiCIASHxIUgCIIQHBIXgiAIQnBIXAiCIAjBIXEhCIIgBEfV4sIYg8FgwJUrV2AwGMAYkzskxUNtFhzUboFDbRYcjDGUl5fDbDajvLxcte2mSnExGo1YtmwZMjIy0Lx5c3Ts2BHNmzdHRkYGli1bBqPRKHeIisOzzVJTU9G+fXukpqZSmzWAd7t16NCB2q0BvNssPT2d2swPPNutV69e2L59O3r16qXedmMqY9u2bSwuLo5pNBqm0WgYAPcP/7u4uDi2bds2uUNVDNRmwUHtFjjUZsERju2mKnHZtm0bi4iIYFqttlbje/9otVoWERGhqi9CLKjNgoPaLXCozYIjXNtNw5g6EnpGoxFt2rSBxWIBx3ENvl6r1UKv16OkpARJSUniB6hAqM2Cg9otcKjNgiOc2001cy5ffvklzGazX18AAHAcB7PZjJUrV4ocmXKhNgsOarfAoTYLjnBuN1WMXBhjyMjIwKVLlwKqnNBoNEhPT8f58+eh0WhEjFB5UJsFB7Vb4FCbBUe4t5sqxMVgMCA1NTWk9zdt2lTAiJQPtVlwULsFDrVZcIR7u6kiLVZTUxPS+6urqwWKRD1QmwUHtVvgUJsFR7i3myrEJT4+PqT3JyQkCBSJeqA2Cw5qt8ChNgscg8GAvLy8kI6h9HbTyR2APzRt2hQdOnQIODcJAO3atYPZbAYAxMbGIiYmRtF5SqEIpc3S09ORnJwsUmTKpmnTpkhPT8elS5cCeh+fB09JSREpMmXCcRzi4+PRvn17XL58OaD3NrY2u3btGnbu3Im8vDz88MMP0Gq1SEhICHgEopZ2U8XIRaPRYMKECUG9b+LEiYiPj4fVasWtW7dQUlICg8EAs9msWlsFfwi2zQBgwoQJYIzB5XL5XcUSDjDGYLfb8dJLLwX13ldffbVRPLgAgNPphMVigclkgtPpxP/7f/8vqOO89tprYd1mly9fxueff46nnnoKQ4cOxZIlS5CQkIB3330XRUVFePfdd4P6/GpoN1VM6APC1IPb7XaYzWaYzWY4HA5oNBro9XrExsZCr9dDq1WF1vqN0WhE69atYbFY/BJS7zbjOM79Po1G4/4JRxwOBxwOBwDAZDKhffv2fl9r/HV04cIFpKSkIDIyMuyuJeCOgDocDtjtdjDGEBERgcjISERGRgbcPzUaDWJjY1WxXiMQGGM4c+YM8vPzkZeXh0uXLkGv1yMrKwtDhgzBwIEDa6URw3mdiypX6HvbI3j/8CtZt2/fXuex7HY7q6ysZNevX2dXrlxhV69eZaWlpay6upo5nU4JP5V4cBzHtmzZwrRard+rf321GcdxzOVyMafTyZxOJ+M4ToZPIw5Op5OZzWZWU1PDbDab+7MFump6+/btzOl0MovFwsxmM7Pb7WHTTnwbVVVVserqamaxWJjL5brrdf62mUajYVqtlm3ZskWGTyM8LpeLHT16lH344YdsyJAhrGvXrqxv375sxowZbNeuXcxisdT7/mCuNTWgKnFh7M4XERMTU+dFy3vwBPIFOBwOVlVVxW7evMmuXLnCrly5wm7evMmqqqpUKzS8IHAc57dvUUNt5i0y/PHViMvlYhaLhdXU1NR7swym3RwOB7NYLMxisTCHwyHVRxIUjuOYzWZjNTU1rKqq6i7xrYtAPLIcDodqH1YcDgfbv38/e+edd1hWVhbr2rUrGzhwIHvnnXfYvn37Av7e62s3vu0Cva/JjerEhTHGpkyZwtLS0lh6enqtL6BDhw5s2bJlzGg0Bn1sp9PJqqurWWlpKbt69Sq7cuUKu3HjBqusrFTNjcJTWHgqKirYsmXLWIcOHQRpM47jVCkynjdNs9nc4MNDsO3GcRyz2+3MbDYzi8WimocUXnSrq6tZVVWVX23kTSBt5nQ6mcPhUMX1Y7Va2a5du9iMGTNY3759WdeuXVlubi774IMP2NGjR0P+jutqt+TkZLZw4cKQ7mtyoJo5Fx6n04nevXtjzJgxmDlzJsrLy1FdXY2EhASkpKQIOifAcRwsFgvMZrN73iIyMhKxsbGIjY1FVFSUYOcSCnbngaHO+RH2f3tFCNVm/PmYx9yMUucbPOdV+LkCfwm23TiOg8PhAMdx7jkKJc5b8W3jcrmg0WgQFRUVcqz+tpnL5XLP4SitbUwmE4qKipCfn4/CwkJYLBakp6djyJAhyM3NRZcuXQSP2bPddDod/vGPf2D48OHo3bu3oOcRG9WJS1FREZ577jls3rwZmZmZkp2XMVZLaDiOg06ncwtNdHS0ZLHUF2N9wiI2Si0AcLlcsNvt7u8sKipK8rhcLhccDgcYY9DpdNDpdLK3DS98nnFFRkZCp5N+hYKSBMZoNKKgoAA7duzAgQMHYLfb0bVrV+Tm5mLIkCFIT0+XNJ5vvvkGFosFv//97yU9b6ioYp2LJxs3bkT79u3RrVs3Sc/LV7fExsaCMQar1Qqz2YyamhpUVVUhIiLC/feYmBhJYwPkFxYA7hELHwtf/SLXaIb9X2mx0+lERESErBWBERERiIiIgNPpdI8QIiMjERERIXksfAxOpxMajcY9ipNzxBkREQGXywWXyyWLwNy+fRv5+fnIz8/H4cOHwXEcHnzwQUyePBmDBw9G69atJY3Hk8zMTKxduxaVlZVITEyULY5AUZW42O12bN26FS+88IKsTzd86aler0fTpk3dQmM2m1FdXQ2tVltLaMSOVQnC4gkfh2fKjE+3SBEj+7+SWb7cPDo6WpancV/odDpERES4S3q1Wq0kN3bPNuFTdDExMYoYQfFILTAlJSXukuHjx49Dq9WiT58+mDVrFgYNGhSS75eQdO7cGTqdDsXFxejfv7/c4fiNMnqcn+zevRs1NTX45S9/KXcotYiJiUFMTAxSUlJgs9ncQlNTU+OuS+fX0oiRn1WSsHjiGZP3aEar1YoSr9PpdK/DiIyMVOS8GD+nwaelbDabaPMxfDrOc64pJiZGlhGTP4gpMIwxXLp0CXl5ecjLy8OPP/6IqKgo9O/fH++//z5ycnIUOTKIiopCp06dSFzEZOPGjejSpQs6duwodyh1Eh0djejoaCQnJ8PhcLiF5vbt24Iv2lSysHjjPZrxTJkJET/HcbDZbLLOqwSKVqtFdHS0WwCsVqsgcx6MMbfIchznPo9Siwm8EVJgGGM4ffo08vLykJ+fj8uXLyM2NhbZ2dl48cUXMXDgQMTGxgoYvTh0794dq1atgsFgQLNmzeQOxy9UIy4mkwn5+fmYOHGi3KH4TWRkJBITE5GYmAin0+kWGoPBAAC1hCbQJ0nvm7Na8B7N8EUAwYqM57yKVqtV9FN5XfDzMfwIw+l0BjUfw3Gcuy34CXolpQQDIRSBcblcOHbsmDvldePGDSQmJmLQoEGYOnUq+vbtq4gCnEDo2LEjoqOjUVxcjJycHLnD8QvVXHX5+fmwWq2KS4n5i06nQ5MmTdCkSRO4XC630JSVlQG4k1rjhaahm4FnaknNaDQaREREBF0AwM9bKG1eJVj4UUug8zH8KIWf1+LTgWp66PBFIALjcDhw+PBh7NixAzt37kR5eTlSU1ORm5uL3Nxc9OrVS3UPHZ7odDrcd999JC5isHHjRvTs2RNt2rSRO5SQiYiIQEJCAhISEuByudwlzhUVFSgvL0dUVJS7IMB7LUa4CIsnniMWfiRTXwGA97yKWtI9/uA5H2O322Gz2XyWLnuXEfPVcGoXWG8iIiLAcRxcLhe0Wm2t695qtWLfvn3Iz8/H7t27UV1djTZt2mDkyJHIzc3F/fffH1b9pHv37jh+/Dhu3ryJli1byh1Og6jiSuTrzt966y25QxGciIgIxMfHIz4+vtaizcrKShiNxlqLNvkbRzh1GG/qKmfWarXuFBj/JBsVFRW2bcGn+JxOp/uHf9BQWhmx2PCfjeM41NTUYO/evcjLy0NRURGsVis6duyIZ555BkOGDEHnzp3D5kHDm/bt2yM2NhYnT54kcRGK7du3g+M4PPHEE3KHIiparRZxcXGIi4urtWizuroaFRUV0Ol0iI+PV8yiTTHxLADgOA5WqxUOhwMRERFhkQLzF51OB61WC4vFAqPRCMYYoqOj3aOUcL2RelJRUYHdu3e7FzU6HA5kZmbi5ZdfRm5uLtq3by93iJKg1WrRtWtXnDp1Crm5uYr/7lXRQzds2IC+ffsqpu5cCjwXbbpcLlitVlitVphMJkUs2pQKfsEfgFqT9RzHqa6YIVC8y4j5qiZedMOZ0tJS98ZaR44cAWMMPXv2xOuvv45HH30Ubdq0CevRWl1kZmbiyJEjKCkpQdu2beUOp14ULy63b9/GgQMHsGDBArlDkQX+JsqPaADAZrPBZDLBYrHIsmhTCuqzbBGrnFkJ8GXE/Cp+X2XEnqXLSrGSEYKff/7ZXTJ8/PhxREREoG/fvnj77bcxaNAgNG3aFMCdPhGOc4/+0K5dOyQkJODkyZMkLqGyefNmaLVaDB8+XO5QJKeuDsSvpQFqb4AmxaJNseEnsvl5FV/rgXwVAIRSzqwEfPl81TVB78tKhhcZNcEYw4ULF9yLGs+dO4fo6GgMGDAACxYsQE5ODpo0aXLX+zznYDz/3RjQaDTIzMzEiRMnMHz4cEV/dsVfjRs2bEB2drbyd10TGH87TlRUFKKiopCUlORz0WZMTAzi4uIUv9NmsJYtSvMzCxRfZcT+TtB7Wsl4+pUp+XMzxlBcXOweoVy9ehVxcXHIycnB+PHjMWDAAOj1+gaP05gFJjMzEwcOHMCVK1ckN9EMBEWLS0lJCY4ePYrly5fLHYqkBNthGlq0ya+liY2NVVTNv2dpMW/1HiiBljPLCS+kntsFx8TEBP25pbKSCRaXy4WjR4+6FzWWlpYiKSkJgwcPxptvvom+ffsGZdPDWwh5Oio3Bu655x6kpKSguLiYxCVYNm3ahJiYGOTm5sodimQI9SRW16LN8vJylJeXIzo6+q4SZ6kRywq/vnJmOW+4/Ofly4j5zyzEU7cvKxneQl8OHA4HDh06hLy8POzatQvl5eVo0aIFBg8ejKFDh6Jnz56CiAG/ENdzsWVjIDMzE4cOHcKIESMU+5kVLS4bN25Ebm6ueyI7nBHTJ8xz0SbHcW6hMRqNqKioqHfRphhIZdkitp+ZP3i7EfOfV6xJeE8rGafTKam1v8Viwb59+5CXl4fCwkJUV1ejbdu2ePLJJ5Gbm4vMzExR0leNUWAyMzNRVFSECxcuoHPnznKH4xPFisvFixdx+vRpTJo0Se5QREdKA0qtVuv3ok0xHIXlsGwR2s/MH/gRhKfPl5S+Z8FayQRKdXU1CgsLkZeXh71798JqtaJTp0547rnnMGTIEGRkZEgi4o1NYFJTU9G8eXMUFxeTuATKhg0bEB8frxofnWCR09nYe9Emvy9NdXU1KisrBd1pUymWLaH6mTWEGNsFB4tY8zHl5eXYtWsX8vLycPDgQTidTnTv3h3jx4/H4MGDkZaWJtyHCIDGJjDdu3dHUVERHA6HbOnP+lCkuDDGsGnTJgwfPjysV6IryTLfcwM0z31pfC3ajI6O9jte79JipVi2CFkAEEgZsRzw8zG8jUww1v43b95079T4/fffAwAeeughTJs2DYMHD1aMHUljEphu3bph586dOHv2rKRbvvuLMq5+L06dOoVLly5h7ty5cociGkoSFm/4EmZfG6D5u2hTTVb4wZYzK3G74PrgS5c9465vPubq1avuCq+TJ09Cp9PhkUcewZw5czBo0CCkpKRI/An8o7EITHJyMlq3bo3i4mISF3/ZuHEjUlJSVLXrWiAoWVh84bkBmveiTV8boHlalgRbWiwH3gUAvkYzdW0XrKbPWNd8jEajwfnz592LGs+fP4+YmBgMGDAAzz77LLKzs5GQkCD3R/CLxiIw3bt3x44dO2C1WhVnA6U4ceE4Dps2bcKIESMUk1YQErUJizd1Ldo0GAy1qqESExMDSp8pCe8CAM91Kbwdj9K3C24Ifj7G4XDghx9+wK5du7Br1y6UlJSgSZMmyMnJwauvvooBAwYo7qblL41BYLp27Ypt27bhzJkz6NGjh9zh1EJxd++jR4/i+vXrqt0UrD7ULize8Is2ExIS3CkzPoXGP0kpcdGmv3huF+xrBb1av0OXy4Xvv/8eeXl52LlzJ0pLS5GcnIysrCxMnz4d/fr182uVvBoId4FJSEhAWloaiouLSVwaYsOGDWjVqhUefvhhuUMRlHATFqD2Gg6tVovmzZu7O7ISF236i6/tgj1HKVKVMwuJ3W7HwYMHkZ+fj127dqGiogItWrTAkCFDkJubi549e7pTmi6XCzabTdHzR4HAL1h1uVxwOp0Bb5usdDIzM7F582aYTCZFrQlUVC93Op3YvHkzRo8eHRYXNU84Ckt9li1KW7TpL95lxHVtFyx2ObNQmM1m98ZahYWFMJlMuPfeezFmzBgMGTIE3bp1u+uzKd1KJhQC2TZZTXTt2hVbtmzBqVOn0Lt3b7nDcaMocTlw4ADKysrCKiUWbsISqGWL56JNzw3QpFq02RChbBesRD+zqqoqFBQUID8/H3v37oXNZkPnzp0xbtw45ObmomPHjg3GpTQrGSEJR4HR6/Xo0KEDiouLSVzqYuPGjUhLS0P37t3lDkUQwklYvEuLg3FZ1mj+uwGa2Is2G0LoMmI5/czKysqwa9cu7NixA4cOHYLL5cIDDzyAV199Fbm5uWjXrl1Qx/Vl7S+VlYyYhKPAZGZmYt26daisrERiYqLc4QBQkLjY7XZs3boV48aNC4svO5yExW63B2yF3xCeizabNm3qFhrPRZt8ibNQG6BJ4fMllZ/Z9evX3Ysajx49Co1Gg169emHGjBkYNGgQWrRoIch5gNrW/mJayUhJuAnMfffdB51Oh1OnTqFfv35yhwNAQeJSUFCA6urqsEiJhYuwSGnZUteiTSE2QPPeLliKMuK6/MyA4Eczly9fdi9qPHXqFCIjI9GvXz/MmzcPjz76KJKTkwX9DJ6IZSUjJ+EkMFFRUejUqRNOnjxJ4uLNpk2b0KVLF2RkZMgdSkiEg7B4WrYIaYXvL3Ut2jSZTD4XbfrCs4yYH6V4bxcsFfUVANR3nTDGcPbsWfeixosXLyImJgZZWVn43e9+h6ysLMTHx0v5UXzOxwRqJaMkwklgMjMz8e9//xtlZWXuLaHlRBFXhNlsRl5eHiZMmCB3KCGhdmFRomVLfYs2eZsafp5Gq9X69PmSyn25IfxxZ+Y4DidOnHDv1FhSUoKEhAQ8+uijmDRpEvr166eIRY0RERHQarV+W8komXARmIyMDERFRaG4uBjZ2dlyh6MMccnLy4PFYlF1Skzt262qwbLFe6dNi8UCk8mEsrIylJaWup+q4+Li3JYsSv0+PEczDocDhw8fxs6dO7Fz504YDAakpKQgNzcXQ4YMQa9evRT5fdRnJaPUdq+LcBAYnU6HLl264OTJkyQuPJs2bUKPHj3Qtm1buUMJCjULi2dpsZxW+IGi0+kQHx+PqKgodzEAP1fjcDgUv2jTZrPh4MGD2LFjB3bv3o3Kykq0bNkSw4cPx+DBg9GjRw/RNhQTGn4+hk+V2Ww26HQ61cTP4ykwWq1Wlf05MzMTx48fx82bN2V3qpa911VWVmL37t2YNWuW3KEEhVqFxdsKP5jSYrnw3i44OjoaCQkJ7rQYv5ZGaYs2TSYT9uzZg/z8fBQWFsJsNiMtLQ1PP/00hgwZgq5du/qsNFOL1Yxn6TK/CyYvMmohIiICHMeptl+np6dDr9ejuLiYxGX79u1wuVx44okn5A4lYNR4AXpbtihhXsUf/C0j9t4AjReaqqoqGI1GSdfSAHcengoKCpCXl4d9+/bBbrejS5cueOGFFzBkyBCkp6f7dACQopxZLAK19lcafH9WY//WarXo1q0biouLkZubK2sssovLhg0b0LdvXzRv3lzuUAJCjReeGuZVvPEuIw5ku+C6Fm3W1NTctQGakJPkBoMBO3fuRF5eHr777ju4XC48+OCDmDhxInJzc9GmTRu/juNPAYBS4edjPNfHqKl0Wc0Ck5mZiSNHjuDnn3+WdapBVnExGAzYv38/5s+fL2cYAaO2Cy5QyxYl4O3zFWoZcV2LNnmHgFAXbV67ds29BuXYsWPQarXo1asXZs6ciUGDBoX88BRsObPc1GUlo4b5GLUKTLt27ZCQkIDi4uLGKy6bN2+GVqvF8OHD5QwjINR0oTHGYLPZVDOvIuV2wUIs2rx06ZK7ZPj06dOIiopCv3798N577yEnJwdJSUmCx+3Lz0wNoxlfVjJqmI9Ro8BoNBp069YNJ0+exLBhw2SLWdZvduPGjcjKyhJ1ZbGQqOUC85yfENKyRSzk3i7Y30WbMTExtRY1Xr58GXq9HtnZ2fj973+PrKwsSS3Pg92eWU48rWQ8/cqUGi+gToHp3r07Dh48iKtXr6J9+/ayxCDbHef69es4cuQIli5dKlcIAaGWC8vbskUOp2F/8NzdkXcjVsJ2wd6LNk0mE7777jvs2rUL+/btw61bt5CYmIhBgwZhypQp6Nu3r+yLGr0LAJTgzlwfarSSUZvA3HPPPUhOTsbJkycbn7hs3LgR0dHRGDp0qFwh+I0aLiiO42Cz2RQ/r+JZRgzAPUpRUiWR0+nEd999h/z8fPeixqZNmyI7OxuPPPKI2yQwJiYGDodDMekd7wIApZczq83an29Dl8vlfiBSMpmZmTh8+DBGjBghS6yyisvgwYMVtXOaN2qwc1GiZYs3SvL5qgur1YoDBw4gLy8Pu3fvRlVVFVq3bo0RI0ZgyJAheOCBB9wPFy6Xy13iXFFRocidNtVUzszPx/CpUSVb+/OFFWrYNjkzMxN79uzBxYsX0alTJ8nPL0svuHTpEk6dOoXXXntNjtP7hRqEhU8rKXVepaHtguXGZDKhsLAQ+fn5KCoqgsViQXp6On7zm98gNzcX9913n8/vPiIiwr0Bmq9Fm3JvgOaJmsqZ1WIloxaBad68OZo3b46TJ082HnHZuHEj4uLi8Oijj8px+gZRurBIaYUfDN5lxPyaGiXEaDQasXv3buTl5WH//v1wOBzo1q0bXnzxReTm5iI9PT2g49W1aFOODdAaor5yZqXcwNUyH6MWgeFHLw6HQ/J0o+TiwhjDhg0bMHz4cNk7my+ULCzeli1RUVGKuSmEsl2w2Ny6dcu9qPHIkSPgOA49evTA66+/jsGDB6N169aCnKeuRZueG6CJsWgzmDi9y5mVVgDAp055KxklWvurQWAyMzOxa9cunDt3Dt26dZP03JJ/U2fOnMGlS5cwZ84cqU/dIEoWFn43SKXNq/A3UbnKiOvj6NGjWLx4MY4dO4aIiAj06dMHb731FgYNGoRmzZqJem7PRZsA7lq0yY94UlJSRI2jIeTcntkffFnJKOmhSukCk5ycjNatW6O4uFhycdEwfnu8EFi2bBk6d+7s12vtdjuqq6t9bmbDP5n7eqqrqKjAr3/964BjC+Tj8a8NplMF8x4+r+zva/mbdyDwqbNAsdlsfsfGV/kEalXOGAt4TuIvf/mL3xvK2Ww2lJeXIz4+HnFxcbU+j8Vicd/4vTEajRg7dmxAcQF3fMT8aWuHwwGLxQKO4wJaaMkLQDAbhPnbD0J9wArmPfx6rIbey3Gc26cs0PPwc36BwAutv8fnOC4ocQlGKAsLC/12fbhx4wZMJhM6duzo9/H51PtDDz0UcGw8goxczp07h/Hjx4d0DJPJhIkTJ8JgMOCZZ57BU089VevvEyZMCEpcAkHqJzXe5t4f6roR8iOH6OhonxepzWYLSlw4jvP7xu99szObzYiOjm6wo1mt1oDjunDhAv7whz8E/D5PlixZgkOHDuHhhx/GG2+8cVe7TZs2LShxcTgcaNKkSYOv0+v1fr3OE8YYSktL3VsNBAovGHX9mydYUQnlwYxPyzWUJtdqtUGnxex2e8DvZYz5feMPZt6KT0UGw61bt9C1a1e/Rr6BTuZXVVVh9erVSExMDElcBBlbeqZDgvnR6XQYN24coqOj8Yc//AHz58/Hl19+6a55D3Uiqq4O45ljDuVHiNiC/bHZbLX+K3ds/BOcxWIRpd1Cvda++OILbNmyBRMnTsTBgwcxZ86cWteZUNea0D82m829NijU2DxHMd7fhdTXP4+nOAn543nsYBDr+wwVjUaDL774AmVlZe5SbqF+1q5dixYtWoQcoyISl1VVVTh69Cj+9Kc/YdSoUfj2228xf/58XLhwQe7QFA/HcYiJiXGnM+SGr+4BQuvUYuBwOLB8+XJ88cUXyM7OxsqVK7F161ZVXGc1NTWiFQGEeu0I9T0HkoYKBJvNJspxQ0GINuvbty++/vprAaL5L4wxlJSUYNiwYSEfSxHiMm3aNOTk5LhXlWdmZmL69On41a9+JdoFFw4o7eYNwD3hqkSWLl2KDh06IC0tDQCQlJSESZMm4eWXXxbsHGJ9J1arVZAFx57xecfqKTKeVjJ1vc7zb6E+jWu1WrhcrpCO4QsxjikEQlwn/fv3R2VlpaDXHH+/FaIPyy4ujDFs374dixcvrvX7F198ETqdDsuXLxek8ZR4IxYKvmMrpSPxE/uhpnGEhDGGf/7zn/jzn/9c60b4/PPPo7S0FGazWZDzCN3ZeRhjgpbue7aB5/yLt3B4i0hdvw8VfgdIoVFiBRePEIIMBDd3WRenT5+u1wk8EGQXF5vNBsbYXdVjGo0Gq1atwieffIIFCxYIdj7vTqVmPDsjv7JZKURGRsJut8sdhpuffvoJGo0G99xzT63fa7VaZGZm3vVwEyxVVVWiibwY5bfe8y+ev/Oet/AeqXjP1YSCVqsVpT8GW8ElNnUVVARKixYtsHfvXgEiusPOnTsxcOBAQY4lu7isXLkSbdq08dnQaWlpWLlyJaqrqwU9p1CTkHLD+4kBd8RF7hSi540nMjJS9ng8mTJlCn71q1/5/O4XLlyI1atXC3Ke6OhoVFZWCnIsMalLSPyZGBdrgloslLImxhshPvPQoUNx+PBhAaK5Q2VlZUgVYp7I3urLly/HO++8U+ff+/btK/pOlUIP8aXC6XS6yyuV1oGUJOCMMZw5cwaTJk3y+fe2bdvC5XIJksZLSkqCyWQK+TieCDWv4XksT+qqFvP1u7r+RshDWlqa2xUjVPhjCGUTI+sdiTGG6upqNOQxRhdv3SjJDqO+FIucXL9+3e1s4AuNRoPU1FSsW7cu5HMptZjBE/67CUQYhC49rismtR1bbjydukPl2rVrAS+Erg9ZxYWfRJUzJ+qrEkaNKOFmrpSCAm9mzZqFESNG1Ntp3n77bcHmXQBhvwex5tLEFoxgELLd1NqXAyUhIQFHjx4N+TibN29Gr169BIjoDrKKy9///nfZdkkjhMfpdN71oCC34DDGcOTIEbz55pv1vi47Oxs1NTWCLFQUGovFoqgRKiEMQl0rjz/+OHbt2hXSMRhjuHnzJnJycgSJCZBZXD777DO8/fbbspzb+4sN5ouWc56mrjy8nDdzl8tV6yao0+lEqRgLpM2rqqoAoEG7Fa1Wi/T0dCxZsiSk2HiEHG1YLBbZt1JWI0oqKPFE6HtG586d3VW3wWKxWAAIm9aVTVwYY6ipqUF2drYk5wLCO/cKwO0eKxYNFT54mwNGRkaKInarVq3yuyPNmzcPjzzyiF/f/eeff47S0tJQw0NUVBRqampCPg6Pw+FAbGysYMdTMkIKAsdxYd/ngf9u9XDs2LGgj7FhwwZ06tRJ0PaSTVz4iho551uUmHP2F1+dUKfTCXoz99yfhTEGm80Gs9ns3qjMF55tKdZ3u3DhQr9yzIwx7NixA++//75fx23ZsiUWLlwYaniIj48XbFEmEJx7dF3HAZT7kCX0Kn0lL6AUmrFjx2LLli1BjV4YYzh37hxGjRolaEyyicunn34akAW0FChhUtxfPNe48AjdkWw2G2w2G6xWKywWC1wuF6KiotwblvmL0O05e/ZsTJw4scHXlZWVAQBSU1P9PrYQbajX6wVPyShVEIREq9UK2m7s/zatawykpaXB5XK5r/lAOHPmDKKjowVPvcomLn/729/8fqJUEkpZE+M9vyEG/K6JwJ2OHxsbi8jISOj1elgsFp8+VUKu2q6LUaNGwWg0Nmh7MX36dAwbNkzyG7OQa47kvs6kRIxV+koQZe/7hRjfqUajQXZ2Nv71r38F9D7GGNavX48xY8YI3layiAtjd/Ya7927txynDwt8PZUJPfLSarXu9SHR0dHu4/Pn9fcpU+h5II1Ggy5duuDjjz+u8zWMMRw6dAhz584V9Nz+IMYIWAk3SbFR2kJgT0J5oOT3q/H0ZxPj+xw4cCCMRqN7ct4fbt26BafTKUoWSZZv88cff1TMVriBoLSnSKluOL5WZUdFRdUaOdTVNnwaTWgWL16Mb7/9ts7z7tu3D3q9XhAn4WARomJMSeafakJoVwOXywWO42oJBP/v+tbK8a8D/vswJpa4aLVadOvWDatWrfLr9YwxfP311xg8eLA48Qh1oEBy8JMmTcK4ceOEOrUo+Lu4UuwbPGMMDoej1iihIZGTohw5KiqqVmdzOp0+28L7dULRtm1bMHZn7wlvGGOYNm0a3nnnHdme+OPj41FeXh7ycaqqqgRzQ1baw5E39X1X/E3acwQgFXzVmaeg8GLjKTr83/kfT+GJiIjw6WAhNCNHjsTVq1f9Gr2Ulpaiuroa/fr1EyUWwcRl8uTJfj1lMcbw448/4o033hDq1ILiz5cuVpWZ58XL/9tms8HhcMBqtd7VqXydn3cjZoyJ+tTrbfPvcDjqnQPi4xHqxqDRaDBu3DiMHz/+rmMajUZUVVXhscceE+RcwZCUlAS73R6wsPIPE/y6BbPZjKSkJMHiUkN6zdeDndPpdPcFvqCkvlSVUA9Y/Dm0Wq1bIPjtifmdG/nz8UIDoJbIeGZoxBbGyMhIZGZm4uuvv673XBzH4Z///CeGDx8u2jUhmLj8+OOPmDFjRoONt379eiQmJqpqUZjYTxz8BcyLCF+ZxT8Z6fV6AP9Ns9TXcSIjI90iJfYOfNHR0e7UGMdxPstleYdks9nsLmUWqoNNmDABV69exblz52r9fvLkyXj88cdlvZFqNBrExMSgtLQUJpOpwc/McRzMZjMMBgNu3boFg8GAsrIywcqQ1YbnSMDpdMLpdCI6Oto998cLMP/A4t2+nqauQsA/TPKCotVq3b/jhcfzb7wQybHcYeTIkSgtLcWJEyd8Xnccx2HDhg2IjY0V1O7FG8Faf9WqVejVqxdGjhyJAQMG+HyN0+nE9OnT8eWXXwp1Wr8JdgW+2PBPPPyTWHR0NDiOc9+0+c4UExMDi8XiHpk05Fxqs9lEt72PjIystTK4rjaOjo6GTqdDREQEampqBGtXnU6H6dOn44UXXsC2bdsQHx8Pg8GAI0eO4MiRI4KcI1h4M0yTyYSKigq4XC40adIEHMfB4XDUmnO02WwoLy93f89JSUnQaDQwGo3u/28saDQad5m955xVdHS0u708H6BcLpd7a21P00XvBb3Bwo9SPOPzFbMv+FGN59/5/ijmd6rT6fDMM8/gq6++AgDcf//97vNZLBZs3rwZ165dwx//+Edx4xDqQMnJyVi2bBleeOEFLF26FK1bt8bt27dhMBgQExODli1b4ssvv0SHDh3Qt29foU7rF4E2IJ9fDfU4/mC1Wt0dIzIy0v0kxJdlel6gWq3WfTOvS1w0Go17MSV/8xcL/kmOz+/W1T58TMCdG4PFYhHsae43v/kNDhw4gHHjxuHtt9/GrFmz8PTTTytiZKzRaBAXF4eoqCjcunULdrsdDofDfX0lJSXB5XK5RSQuLq5Wu3hvoNcY8NxkLjIy0ucN2nvEwI9uXC6X+3dCEmzhkff1HRERIZk9U7t27fD0009j/fr1uHLlCh566CFUVlZi9+7dSEpKwgsvvCC664Ng4sIYw+OPPw6j0YiPP/4YDocDcXFxSExMhNVqRVVVFdq1a4dvv/3W/XqpEOpcYsQcExPjMyfr63f86IXvPPVVaAmBP5+XX/Oi1+v9en10dDRMJlNIm5t5n+fjjz/G/PnzMWPGDKSnp2PmzJmyTV77Om9kZCRatmwJs9mMhIQEREVFwWQywWg0QqPRoFmzZrXE0N9iEiFjlBvP695TOLz/7gutVusuHHG5XO6RYUPv8we+HwrZZkKt52noGB07dsQLL7yA3bt3Y/369dDpdHj44YfRq1cv0Xb+9EQQcUlOTsb27dsB3Hnaeumll2Cz2aDX6xEVFQWXywWr1Yr4+HgcOHAgqHN07dpViFAVBf8EG8jTDD+68fc9oTx1+VsQwKcp/H19KNVPycnJ2Llz512/79+/P7p27YrExEQUFBQEfXwAuO+++4J6n1arrbdKhxdUfrTapEkT9zXg79qEUB4cxE6vhXJ87y27NRpNUA8fnvMhnu8PZdmD0MLiecxg2yw2NhY//vijX6/t0qUL0tLSoNPpEBUVddccZV20bNkyqNh4NEyAlpOiFp9PwQSKVE9pSp3TAcIrNrrWwuv7BJQbm1LjAqRzfA5FlAURl0BwOByorKxEUlKS4vaoEHLhlRh4lzUqBYvFgqioKMX5OFksFpSXl6NVq1aKazeTyQSHw4HExETFXW/8ug6lxcWjxH7AFxgorQ8Ad3aYNJlM6NSpk6TnlfwbKi4uxi9+8Qv06NEDW7dulfr0DRKKzYOYcBwHi8WiuD0q+HJQJd2IXC4XVqxYgd69e2PmzJmoqKiQO6S7YIyhqqoKN27cEG2nyVBQ2nXGw5fYKy0+pcUD3Hm4WrVqFf72t7/h/Pnzkt/XJB+5AEBlZSWmT5+OrVu34te//jXmzJnjXsshN56LppQELy56vV4xsTmdTlgsFkRHRytmLca1a9cwbdo0nDx5EuPHj8cf//hHRT5NAndG8bdv34bT6URycjISEhLkDskNX4KrlGuNhxcXz9JkueEXSwq5/3yoXLlyBWvXroXT6cTIkSPRuXNnyWOQRVyAOzfxVatWYc6cOWjdujX+/Oc/o0uXLnKEchdKTAsoTVwYYzCZTG63ZCWwdetWvPPOO0hISMCiRYvw4IMPyh1SgzDGUFFRgerqauj1ejRr1kwx3y+fflJaP1CSuPAFOfzyAbnhOA4FBQXYs2cP0tLSMHr0aNkeWmQTF54LFy7g1VdfxYULFzBz5kyMGzdO9ouZH70oSWCUJi5WqxVOp9O9NkNOzGYz5s+fj3Xr1uGxxx7DnDlzFDUK8AeLxQKDweCzNFkueOsaJQmM0sSFr9pUwui4oqICa9aswfXr1zFo0CD0799fXpcKucUFuJO3//DDD/H3v/8djz76KBYvXiz7AjKlpceUJC58OiwmJqZBpwCxOX36NKZOnYrS0lK89dZbGDlypGJuhIHicrlgMBhgtVqRmJioiMl+fi5B7muOR0nioqR02MmTJ/Gf//wHsbGxGDt2LFq3bi1rPIBCxIVn9+7deOONN6DVavHxxx9j4MCBssajpI6lFHHh02ERERGyzpPxxntLlixBp06dsGjRIqSlpckWj5BUVVWhoqIC0dHRaNasmaxVlXx6TCnzL0oRF6Wkw+x2O7Zs2YLjx4+je/fuGDFihGAu2qGiKHEBgNu3b2Py5MnYs2cPXnzxRUybNk3Wp2OlzL8oRVx4U00502EGgwEzZ87Evn378Lvf/Q6TJk2SfQQlNDabDQaDARzHISUlRdZ9aZQ0/6IUceErJOVMh12/fh1r1qxBTU0NRowYgfvvv1+2WHyhOHEB7lxAf/vb3/Dhhx+iS5cuWLFiBdq3by9LLEpJjylBXHjXZr1eL9vT9J49ezBz5kxoNBosWLAA/fv3lyUOKeA4DuXl5TCZTIiLi0NKSops3z0//yL33IISxIU3mZWrDzDGsH//fuzatQstW7bEmDFjkJKSIkss9aFIceE5efIkJkyYgNLSUsybNw9jx46V5clJCekxucWF4ziYTCZERkbKMtlst9vx8ccfY+XKlRg4cCDmz5+vyA4lBiaTCeXl5dBqtWjWrJlsaQ8llCfLLS58OkyueZaamhqsW7cOly5dQv/+/fHoo4/KLvh1oWhxAe50rLlz5+Lf//43fvnLX2L+/PmyVALJnR6TW1z4fVhiY2Mlb4PLly9jypQpuHjxIt544w08++yzsqdnpMbpdMJgMMBmsyEpKQmJiYmSx6CE9Jjc4iJnOuzcuXPYsGEDtFotRo8eLVs2x18ULy48GzduxIwZM5CUlIQVK1agZ8+ekp5f7vSYnOJit9ths9kQGxsraadijGHNmjVYsGABWrVqhY8++ihoU8lwgDGGyspKVFZWIiYmBs2aNZP8Jid3ekxOcZErHeZ0OpGXl4fvvvsOnTp1wsiRIxWztqw+VCMuAFBSUoIJEybg+PHjmDx5MsaPHy/pRS5nekwucXG5XDCbzYiKipI0HVNVVYU5c+Zgx44dGDt2LN58803FuDjIjdVqhcFgAGMMzZo1k7xd5EyPySUucpUd3759G2vWrIHBYMDQoUPRu3dvyc4dKqoSF+COii9btgx/+tOf0Lt3byxduhStWrWS7PxypcfkEheTyQSNRiPpk9LRo0cxbdo01NTUYN68eRg6dKhk51YLHMehrKzMvUdMcnKyZNeknOkxOcRFrrLj77//Htu2bUNycjLGjBmDFi1aSHZuIVCduPAcOnQIEydOhNlsxqJFizBs2DBJzivX6n05xMVms8FutyMuLk6Sc7pcLnz66af49NNP0aNHD3z44YeSPjiokerqalRUVECn0yE1NVWykmy50mNyiIvUq/AtFgs2bdqEM2fO4OGHH8bQoUNVWWqvWnEBAKPRiOnTp2Pbtm145plnMHv2bElSBHLMv0gtLnw6TCpTyuvXr2PatGk4fvw4xo8fjxdffFGxVTBKQy4DTDnSY1KLi9TpsKtXr2Lt2rWw2+0YOXKkqucYVS0uwJ0b/TfffIN33nkHbdu2xYoVKyQxwJQ6PSaluEhtSrl9+3bMmTMH8fHxWLRoEXr06CH6OcMNTwPM2NhYNG3aVJLrROr0mJTiImU6jOM4FBYWoqioCPfeey9Gjx6NJk2aiHpOsVG9uPCcP38eEyZMwMWLFzFr1iw8//zzol7wUqfHpBQXqUwpLRYLFixYgDVr1mD48OGYO3eu6gwnlYbUBphSm1tKKS5SpcOMRiPWrFmDa9eu4dFHH8WAAQPCotQ+bMQFuDNHsGDBAvzP//wPBg8ejEWLFolqgCllekwqcZHKlPLMmTOYOnUqbty4gVmzZuHJJ58Miw6lBKQ2wJQyPSaVuEiVDisuLsZ//vMf6PV6jBkzBm3atBHtXFITVuLCs2vXLrzxxhvQ6XT4+OOPMWDAANHOJVV5shTiIoUpJcdx+Oqrr7BkyRJ07NgRixYtUvxiMLVSWVkJo9EougGmlOaWUoiLFOkwu92OrVu34tixY8jMzMQTTzyhGMNJoQhLcQGAW7duYfLkydi3bx9eeuklTJkyRbQncSnmX6QQF7FNKcvKyjBz5kzs3bsXzz//PCZNmqSYHSzDFakMMKWaf5FCXMRehX/jxg2sXr0a1dXVGDFiBB544AFRziM3YSsuwJ0L8a9//SsWLlyIrl27YsWKFaLYskuRHhNbXMQ2pdy3bx9mzJgBxhgWLFgg6miSqI1UBphSlCeLLS5irsJnjOHAgQPYuXMnWrRogbFjx4a1P15YiwvPiRMnMGHCBNy+fRvvvvsuRo8eLfjTldjpMTHFheM4mM1m6HQ6wSeA7XY7li5dii+//BIDBgzA/PnzZd8IrrFiMplQVlaGiIgIpKamijJqFHv+RUxxEdOU0tNwsl+/fhg0aFDYl9o3CnEB7nSst99+G6tXr8bIkSMxf/58xMfHC3oOMdNjYoqLWKaUly9fxtSpU3H+/Hm34aTcWxc0djwNMJOTkwUvdxU7PSamuIiVDjt//jzWr18PrVaLJ598Eunp6YIeX6k0GnHh2bBhA2bOnInk5GSsWLFC0DUVYqbHxBIXMUwpGWNYt24d3n//fbRq1QqLFi2SZO0R4R9iG2CKmR4TS1zESIc5nU7k5+fj0KFDyMjIwKhRo1RhOCkUjU5cAODnn3/GhAkTcOLECbz++ut45ZVXBOsIYqXHxBAXMUwpq6urMXfuXGzbtg1jxozBjBkzyHBSoYhpgClWekwMcRGj7NhgMGD16tUwGAwYMmQI+vTpI8hx1USjFBfgzlPF0qVL8ac//Ql9+vTBsmXL0LJlS0GOLUZ6TAxxMZlMACBYBdEPP/yAadOmuQVm+PDhghyXEA+O42AwGGCxWAQ1wBQrPSa0uIhRdnz06FFs3boVSUlJGDt2rOoMJ4Wi0YoLz8GDBzFx4kRYrVYsWrRIEAdeMVbvCy0uQppSulwufP755/jkk0/wwAMPYOHChbjnnntCjpGQDjEMMMVIjwktLkKuwrdardi4cSPOnDmDhx56CMOGDVOl4aRQNHpxAYCKigpMnz4d27dvx3PPPYe33nor5KopoedfhBQXIU0pb9y4genTp+OHH37Ayy+/jJdffjnsq2DCFTEMMIVOjwkpLkKmw3766SesWbMGdrsdv/zlL2mOESQubhhj+Ne//oV58+bh3nvvxYoVK0J2JBUyPSaUuAhpSrljxw68/fbbiIuLw8KFC/HQQw+FdDxCfoQ2wBQ6PSaUuAiVDuMNJ/fs2YN27dqFheGkUJC4eHHu3DlMmDABly5dwuzZs/Hcc88F3SmETI8JJS68KWVsbGzQx7FYLPjggw+wevVqDB06FO+88w51qDDDbDajrKxMEANMIc0thRIXIdJhRqMRa9euRUlJCXJycjBw4EDyx/OAxMUHNpsN77//Pr788kvk5uZi0aJFQa+kFSo9JoS4CGFK+eOPP2LKlCm4ceMGZsyYgTFjxlCHClOENMAUKj0mhLgIkQ47deoUNm3ahJiYGIwZMwZt27YN6jjhDIlLPeTn57s9yZYuXYr+/fsHdRwhypNDFZdQTSkZY/jnP/+JJUuWoEOHDvjoo4/IcLKRIIQBplDmlqGKS6jpME/DyW7duuGJJ54QfVsDtULi0gClpaWYPHky9u/fj1deecXtthwooc6/hCouoZhSlpeXY9asWSgqKsJvf/tbTJ48mQwnGxlCGGAKMf8SqriEsgr/xo0bWLNmDaqqqvD444/jwQcfDPgYjQkSFz/gOA6fffYZPvroI3Tr1g0rVqzAvffeG9AxQk2PhSIuoZhS7t+/H2+++SYYY5g/fz4GDhwY0PuJ8MHTADM+Ph7JyckBX4uhlieHIi7BrsJnjOHgwYPIz89HixYtMGbMGPLH8wMSlwA4duwYXnvtNRgMBrz33nsYPXp0QO8PJT0WrLgEa0rpcDiwdOlSfPHFF+jXrx8WLFiAZs2aBRw3EX6EaoAZyvxLsOISrCllTU0N1q9fj4sXL+KRRx7B4MGDqdTeT0hcAsRkMmH27NlYs2YNRo0ahffffz8gA8xg02PBikswppRXrlzB1KlTce7cObz++ut47rnnyHCSqIXT6cTt27dht9sDNsAMJT0WrLgEkw67cOEC1q9fDwB48skn0aFDh4BibeyQuATJhg0bMGPGDDRt2hTLly/32wAz2PRYMOISqCklYwwbNmzAe++9hxYtWmDRokXo2rVrQHESjQfGGIxGI6qqqgI2wAw2PRaMuASaDnO5XMjPz8fBgweRkZGBkSNHirbJWjhD4hICP/30EyZMmIDi4mK8/vrrfq9ODyY9Fqi4BGpKWV1djXnz5mHLli148sknMXPmzEbl4EoET7AGmMGkxwIVl0DLjg0GA9asWYPbt283WsNJoSBxCRGn04klS5bgk08+Qd++fbF06VK/DDADTY8FKi6BmFIeO3YMU6dORVVVFebOnYvHHnvMr5gIgsflcqGsrCwgA8xg0mOBiEugZcdHjx7Ftm3b0KRJE4wdO1YwI9vGComLQOzfvx+TJk2C3W7HokWLMGTIkHpfH+jq/UDExV9TSpfLhb/+9a/45JNP0L17dyxcuBCtW7duMBaCqAveADMyMhLNmjVrcLFuoOmxQMTF31X4VqsVmzZtwunTp9GzZ08MHz68URtOCgWJi4BUVFRg2rRp2LFjB377299i1qxZ9VZoBTL/4q+4+GtKefPmTUyfPh1Hjx7FSy+9JOieNkTjxm63w2AwwOl0IiUlpcGCl0DSY/6Ki7/psJ9++glr166FzWbDL37xC5pjFBASF4HhV7K/9957SEtLw4oVK9C5c+c6X+9veswfcfHXlDI/Px+zZ8+GXq/HwoUL8fDDD/v34QjCTwIxwAwkPeaPuPiTDuM4DkVFRSgqKkLbtm0xevRoJCYmBvYhiXohcRGJs2fPYsKECbhy5QreeuutOg0w/U2P+SMuDZlSWq1WfPDBB/jf//1f5ObmYt68edShCFHx1wDT3/SYP+LSUDqssrISa9asQUlJCbKzszFw4EAqtRcBEhcRsVqteP/997Fy5UoMHToUCxcuRHJy8l2v8yc91pC4NGRKefbsWUyZMgXXr18nw0lCUrwNMJOSkup8XUPpsYbEpaF02OnTp7Fx40YynJQAEhcJyMvLw9SpUxEVFYVly5bhkUceues1DZUn1ycu9ZlS8vvULF68GO3bt8dHH32E9PR0gT4ZQfhPQwaY/phb1icu9aXDHA4Htm7dih9++IEMJyWCxEUibt68iUmTJuHgwYMYP348Xn/99bs6V33zL/WJS12mlOXl5XjrrbdQWFiIZ599Fq+//rpfa14IQiwaMsBsaP6lPnGpaxX+zZs3sXr1alRVVeGxxx7ze8EzERokLhLicrnw2WefYfHixejevTuWL1+Odu3auf9eX3qsLnGpy5Ry//79mDFjBjiOw3vvvYfs7GxxPxxB+Im3AWZKSkotIalv/qUucfG1Cp8xhkOHDiE/Px+pqakYO3YsGU5KCImLDBw7dgwTJkxAWVkZ5s+fj1GjRrn/Vld6zJe4+DKldDgcWL58Of7xj3+gX79+mD9/PlJTU6X5YAQRADU1NSgvL/dpgFnX/IsvcfFlSmkymbB+/XpcuHCBDCdlgsRFJmpqavDWW29h3bp1GD16NN577z13isA7PcYYw+3bt2EwGNCsWTOkpqZCo9HcZUp59epVTJ06FWfPnsWkSZPw/PPPUxUMoWgcDgcMBgMcDgeSkpLcBpi+0mN8PygvL0dKSoq7H3inwy5evIh169YBAEaNGoWOHTvK8+EaOXTnkYn4+HgsXboUS5cuxfbt2/HYY4/h+PHjAACNRuM2BVy2bBkyMjLQokULdOvWDS1atEBGRgYWL16MsrIy94hlw4YNGDNmDGpqavD1119j3LhxJCyE4omMjETLli2RkJCAiooK3Lp1yz1q0Wg04Djurn7QpUsXdz/4+OOPYTQaERERAZfLhR07duCrr75Cq1at8Morr5CwyAiNXBTA1atX8dprr6G4uBhTpkzBSy+9hO3bt2Ps2LGwWCwA7jy1eRMbG4uvvvoK+/fvx5YtWzBq1CjMmjWLDCcJVcIbYAJA06ZNodfrsWXLFjz11FMN9oMvvvgC5eXluHXrlttwkkrt5YXERSE4nU4sXrwYf/nLX9C+fXsUFRW5J/jrgh/hdO7cGUuWLMHjjz8uYcQEITyeBpiHDx/G008/DcC3qPDwIvLKK69g9uzZZDipEEhcFMa2bdswYsQI98S+P+j1ely/fr3OxWkEoTZ+/vlndO7cGVartV5h4dFoNNDr9bh27Rr1A4VASXmFcfbs2YCEBbiTTli5cqVIERGE9KxduxYWi8UvYQHujGwsFgv1AwVBIxcFwRhDRkYGLl265HenAu48taWnp+P8+fOUZyZUD/WD8IDERUEYDIaQ1qQYDAZaJEaoHuoH4QGlxRRETU1NSO+vrq4WKBKCkA/qB+EBiYuCaGhTpYZISEgQKBKCkA/qB+EBiYuCaNq0KTp06BBwvlij0aBDhw5ISUkRKTKCkA7qB+EBiYuC0Gg0mDBhQlDvfe2112gSkwgLqB+EBzShrzCMRiPatGkDi8XiV0myVquFXq9HSUkJ1fcTYQP1A/VDIxeFkZSUhDVr1jS4Ix8At6nf2rVrqUMRYQX1A/VD4qJAhg0bhs2bN0Ov1/vcPIz/He+9NHToUJkiJQjxoH6gbkhcFMqwYcNQUlKCpUuX3rUtcXp6OpYuXYpr165RhyLCGuoH6oXmXFQAYwzl5eWorq5GQkLCXTv3EURjgPqBuiBxIQiCIASH0mIEQRCE4JC4EARBEIJD4kIQBEEIDokLQRAEITgkLgRBEITgkLgQBEEQgkPiQhAEQQgOiQtBEAQhOCQuBEEQhOCQuBAEQRCCQ+JCEARBCA6JC0EQBCE4JC4EQRCE4JC4EARBEILz/wEM4xizPo6qigAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=10, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.01, lamb_entropy=2.);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7626a0bf",
   "metadata": {},
   "source": [
    "$G=20$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0887f18d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 5.14e-02 | test loss: 5.50e-02 | reg: 7.70e+00 : 100%|██| 20/20 [00:16<00:00,  1.23it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=20, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.01, lamb_entropy=2.);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c14919f1",
   "metadata": {},
   "source": [
    "### Parameter 4: seed. \n",
    "\n",
    "Previously we use seed = 0. Below we vary seed."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8debdf5",
   "metadata": {},
   "source": [
    "${\\rm seed} = 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8fe1c782",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 5.58e-02 | test loss: 5.50e-02 | reg: 8.48e+00 : 100%|██| 20/20 [00:13<00:00,  1.50it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=1, noise_scale_base=0.0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.01, lamb_entropy=10.);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd5156bf",
   "metadata": {},
   "source": [
    "${\\rm seed} = 42$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e7d3ca9f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 1.43e-01 | test loss: 1.25e-01 | reg: 1.85e+01 : 100%|██| 20/20 [00:12<00:00,  1.65it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=42, noise_scale_base=0.0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.01, lamb_entropy=10.);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bbddc95",
   "metadata": {},
   "source": [
    "${\\rm seed} = 2024$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "01dd251f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 1.50e-01 | test loss: 1.39e-01 | reg: 2.37e+01 : 100%|██| 20/20 [00:12<00:00,  1.57it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=2024, noise_scale_base=0.0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.01, lamb_entropy=10.);\n",
    "model.plot()\n",
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1692e33b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
